{"id":89134,"date":"2021-08-13T15:45:04","date_gmt":"2021-08-13T20:45:04","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=89134"},"modified":"2026-03-26T11:50:36","modified_gmt":"2026-03-26T16:50:36","slug":"secants-chords-and-tangents","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/secants-chords-and-tangents\/","title":{"rendered":"Secants, Chords, and Tangents"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_5XCsNNouB74\" style=\"position: relative;\">\n\t\t\t<picture>\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.webp\" type=\"image\/webp\">\n\t\t\t\t<source srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" type=\"image\/jpeg\"> \n\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" loading=\"eager\" id=\"videoThumbnailImage_5XCsNNouB74\" data-source-videoID=\"5XCsNNouB74\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Secants, Chords, and Tangents Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Secants, Chords, and Tangents\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_5XCsNNouB74:hover {cursor:pointer;} img#videoThumbnailImage_5XCsNNouB74 {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/02\/1737-thumb-final-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_5XCsNNouB74\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_5XCsNNouB74\" style=\"display: none;position: absolute;top: -24px;width: 100%;text-align: center;\"><span style=\"font-style: italic;font-size: small;border-top: 1px solid #fc0;\">Having trouble? <a href=\"https:\/\/www.youtube.com\/watch?v='+videoId+'\" target=\"_blank\">Click here to watch on YouTube.<\/a><\/span><\/div>';\n\t\t\t\tlet tag = document.createElement(\"iframe\");\n\t\t\t\ttag.id = \"yt\" + videoId;\n\t\t\t\ttag.src = \"https:\/\/www.youtube-nocookie.com\/embed\/\" + videoId + \"?autoplay=1&controls=1&wmode=opaque&rel=0&egm=0&iv_load_policy=3&hd=0&enablejsapi=1\";\n\t\t\t\ttag.frameborder = 0;\n\t\t\t\ttag.allow = \"autoplay; fullscreen\";\n\t\t\t\ttag.width = this.width;\n\t\t\t\ttag.height = this.height;\n\t\t\t\ttag.setAttribute(\"data-matomo-title\",\"Secants, Chords, and Tangents\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_5XCsNNouB74\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_5XCsNNouB74\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_5XCsNNouB74\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction sAp_Function() {\n  var x = document.getElementById(\"sAp\");\n  if (x.style.display === \"none\") {\n    x.style.display = \"block\";\n  } else {\n    x.style.display = \"none\";\n  }\n}\n<\/script><\/p>\n<div class=\"moc-toc hide-on-desktop hide-on-tablet\">\n<div><button onclick=\"sAp_Function()\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2024\/12\/toc2.svg\" width=\"16\" height=\"16\" alt=\"show or hide table of contents\"><\/button><\/p>\n<p>On this page<\/p>\n<\/div>\n<nav id=\"sAp\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Secant\" class=\"smooth-scroll\">Secant<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Chord\" class=\"smooth-scroll\">Chord<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Inscribed_Angle\" class=\"smooth-scroll\">Inscribed Angle<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Intercepted_Arc\" class=\"smooth-scroll\">Intercepted Arc<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Central_Angle\" class=\"smooth-scroll\">Central Angle<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Tangent_Lines\" class=\"smooth-scroll\">Tangent Lines<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Secants,_Chords,_and_Tangent_Practice_Questions\" class=\"smooth-scroll\">Secants, Chords, and Tangent Practice Questions <\/a><\/li>\n<\/ul>\n<\/nav>\n<\/div>\n<div class=\"accordion\"><input id=\"transcript\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"transcript\">Transcript<\/label><input id=\"PQs\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQs\">Practice<\/label>\n<div class=\"spoiler\" id=\"transcript-spoiler\">\n<p>Hello! Today we\u2019re going to explore what can happen when a circle and a line or two lines meet.<\/p>\n<p>Let\u2019s start by defining the vocabulary we\u2019ll need.<\/p>\n<h2><span id=\"Secant\" class=\"m-toc-anchor\"><\/span>Secant<\/h2>\n<p>\nA line cutting across a circle that touches two points on the outside of the circle is a secant to the circle. <\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-90052\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-1.png\" alt=\"Image of a secant in a circle.\" width=\"388.5\" height=\"218.5\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-1.png 877w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-1-300x224.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-1-768x574.png 768w\" sizes=\"(max-width: 877px) 100vw, 877px\" \/><\/p>\n<h2><span id=\"Chord\" class=\"m-toc-anchor\"><\/span>Chord<\/h2>\n<p>\nHere is an example of that. We can see that the line intersects the outside of the circle at two points and creates a <strong>line segment<\/strong> between those points, which is highlighted in red. That line segment is called a <strong>chord<\/strong>. <\/p>\n<h2><span id=\"Inscribed_Angle\" class=\"m-toc-anchor\"><\/span>Inscribed Angle<\/h2>\n<p>\nWe can also have more than one secant to the circle interacting with each other, like this: <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/image_2023-09-25_114958303.png\" alt=\"\" width=\"278.28\" height=\"308.16\" class=\"aligncenter size-full wp-image-197891\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/image_2023-09-25_114958303.png 773w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/image_2023-09-25_114958303-271x300.png 271w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/09\/image_2023-09-25_114958303-768x850.png 768w\" sizes=\"(max-width: 773px) 100vw, 773px\" \/><\/p>\n<p>Now our two chords have created an <strong>inscribed angle<\/strong> in our circle, which we\u2019ve labeled with an <span style=\"font-style:normal; font-size:90%\">\\(x\\)<\/span> and a degree symbol.<\/p>\n<h2><span id=\"Intercepted_Arc\" class=\"m-toc-anchor\"><\/span>Intercepted Arc<\/h2>\n<p>\nAcross from the angle is the part of the circle between the points where the chords intersect the circle, highlighted in yellow. This is the <strong>intercepted arc<\/strong>. We can find the measure of our inscribed angle <span style=\"font-style:normal; font-size:90%\">\\(x\\)<\/span> if we know the length of the intercepted arc in degrees.<\/p>\n<h2><span id=\"Central_Angle\" class=\"m-toc-anchor\"><\/span>Central Angle<\/h2>\n<p>\nThe intercepted arc is the same measure as the <strong>central angle<\/strong> that uses the same two points as our inscribed angle, but with its vertex at the center of the circle. <\/p>\n<p>The central angle measures 120\u00b0, so our intercepted arc also measures 120\u00b0. Notice how the central angle is quite a bit \u201cwider\u201d than our inscribed angle. That\u2019s because it is! In fact, it\u2019s exactly twice as wide. That means we can find our inscribed angle by dividing our central angle by two, which means our inscribed angle is <span style=\"font-style:normal; font-size:90%\">\\(120^{\\circ}\\div 2\\)<\/span>, or 60\u00b0! <\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-90058\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-2.png\" alt=\"Image of chords coming together and forming angles inside of a circle. First set is 60 degrees, second is 120 degrees, and third is 120 degrees. \" width=\"388.5\" height=\"218.5\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-2.png 986w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-2-300x227.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-2-768x580.png 768w\" sizes=\"(max-width: 986px) 100vw, 986px\" \/><\/p>\n<p>The central angle is always twice as big as the inscribed angle when our inscribed angle has its vertex on the circle itself. This also means we can find the central angle or the intercepted arc easily if we know the measure of the inscribed angle\u2014all we need to do is double the measure of the inscribed angle!<\/p>\n<p>But what if our two secant lines meet at a vertex that is inside or outside the circle instead of directly on it? <\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-90061\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-3.png\" alt=\"Image of 2 secants that meet at the vertex in the inside of the circle.\" width=\"388.5\" height=\"218.5\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-3.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-3-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-3-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-3-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-3-1536x864.png 1536w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/p>\n<p>Each one of these has a formula for finding the measure of <span style=\"font-style:normal; font-size:90%\">\\(x\\)<\/span> if we know the measure of our intercepted arcs in degrees. Let&#8217;s start when our inscribed angle is inside the circle. In this case the measure of the inscribed angle is half of the sum of the measures of the intercepted arcs (in this case, <span style=\"font-style:normal; font-size:90%\">\\(a^{\\circ}\\)<\/span> and <span style=\"font-style:normal; font-size:90%\">\\(b^{\\circ}\\)<\/span>). <\/p>\n<p>So if we know that <span style=\"font-style:normal; font-size:90%\">\\(a^{\\circ}\\)<\/span> measures 140\u00b0 and <span style=\"font-style:normal; font-size:90%\">\\(b^{\\circ}\\)<\/span> measures 60\u00b0, we simply add them together and take half of that: <\/p>\n<div class=\"examplesentence\">\\(\\frac{1}{2}(a^{\\circ}+b^{\\circ})=x^{\\circ}\\)<br \/>\n\\(\\frac{1}{2}(140^{\\circ}+60^{\\circ})=100^{\\circ}\\)<\/div>\n<p>\n&nbsp;<br \/>\nIf our inscribed angle ends up outside the circle, it works similarly, but we need to use <em>subtraction<\/em> instead of addition before multiplying by <span style=\"font-style:normal; font-size:90%\">\\(\\frac{1}{2}\\)<\/span>. <\/p>\n<p><img decoding=\"async\" class=\"aligncenter size-full wp-image-90067\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-4.png\" alt=\"Image of 2 secants with the vertex meeting outside the circle. The first arch is 30 degrees, and the second is 100 degrees.\" width=\"388.5\" height=\"218.5\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-4.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-4-300x168.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-4-1024x575.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-4-768x431.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords-4-1536x862.png 1536w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/p>\n<p>Our secants create two intercepted arcs between them. Here they\u2019re again shown as <span style=\"font-style:normal; font-size:90%\">\\(a^{\\circ}\\)<\/span> and <span style=\"font-style:normal; font-size:90%\">\\(b^{\\circ}\\)<\/span>. <\/p>\n<p>If we know the measure of the intercepted arcs in degrees, we can plug them in to find the measure of <span style=\"font-style:normal; font-size:90%\">\\(x^{\\circ}\\)<\/span>: <\/p>\n<div class=\"examplesentence\">\\(\\frac{1}{2}(a^{\\circ}-b^{\\circ})=x^{\\circ}\\)<br \/>\n\\(\\frac{1}{2}(100^{\\circ}-30^{\\circ})=35^{\\circ}\\)<\/div>\n<p>\n&nbsp;<br \/>\nWe can do a little common sense check to make sure we\u2019re using the right version of this formula. If we accidentally used the addition formula, we would end up with an angle measuring 65\u00b0, which appears to be way too big for our little angle. Be careful, though. Problems on the standardized tests are sometimes not drawn to scale &#8211; watch for a warning to that effect on any problem you do. <\/p>\n<h2><span id=\"Tangent_Lines\" class=\"m-toc-anchor\"><\/span>Tangent Lines<\/h2>\n<p>\nWhen a line and circle interact, sometimes secants aren&#8217;t created. If a line passes by a circle and only touches it in one point, it creates what we call a line that is a <strong>tangent<\/strong> to the circle. The point where the line and the circle touch is called the <strong>point of tangency<\/strong>.<\/p>\n<p>We see the word <em>tangential<\/em> outside of math sometimes too, describing a topic that is only slightly related to the topic being discussed. Here it means the line that is touching the circle in the slightest way possible &#8211; only at one point. <\/p>\n<p>Anyway, looking closely at our diagram, we can see a radius of the circle meeting our tangential line at a 90\u00b0 angle. For our line to be truly tangent, this must be true. If our line isn\u2019t exactly perpendicular to the radius at the point of tangency it will actually touch the circle twice, though possibly very close together. This would actually create a secant instead of a tangent line. We can see that by zooming in on a circle that shows the angles that are just a few degrees away from 90\u00b0: <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-4.png\" alt=\"Image of secant interacting with a curve, which is at 93 degrees.\" width=\"388.5\" height=\"218.5\" class=\"aligncenter size-full wp-image-90070\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-4.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-4-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-4-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-4-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/08\/Tangents-Secants-and-Chords.-4-1536x864.png 1536w\" sizes=\"(max-width: 1920px) 100vw, 1920px\" \/><\/p>\n<p>Even if the angle were even closer to 90\u00b0, such as 90.1\u00b0 and 89.9\u00b0 this would still happen, though it would be really hard to show on a diagram! <\/p>\n<p>I hope this video on secants, chords, and tangents was helpful! Thanks for watching, and happy studying!<\/p>\n<ul class=\"citelist\">\n<li><a href=\"https:\/\/www.mathopenref.com\/secantangles.html\"target=\"_blank\">\u201cIntersecting Secant Angles Theorem &#8211; Math Open Reference.\u201d n.d<\/a><\/li>\n<li><a href=\"https:\/\/www.storyofmathematics.com\/intercepted-arc\"target=\"_blank\">\u201cIntercepted Arc \u2013 Explanation &#038; Examples.\u201d n.d. The Story of Mathematics &#8211; a History of Mathematical Thought from Ancient Times to the Modern Day<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Secants,_Chords,_and_Tangent_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Secants, Chords, and Tangent Practice Questions <\/h2>\n\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #1:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nMatch the correct name to each line. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Secant-chord-and-tangent-circle-example-1.svg\" alt=\"A circle with two intersecting chords labeled A and B inside, and a tangent line labeled C touching the circle at one point.\" width=\"299\" height=\"266\" class=\"aligncenter size-full wp-image-287558\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">A: Secant<br>\r\nB: Chord<br>\r\nC: Tangent<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-2\">A: Chord<br>\r\nB: Secant<br>\r\nC: Tangent<\/div><div class=\"PQ\"  id=\"PQ-1-3\">A: Tagent<br>\r\nB: Chord<br>\r\nC: Secant<\/div><div class=\"PQ\"  id=\"PQ-1-4\">A: Secant<br>\r\nB: Tangent<br>\r\nC: Chord<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-1\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-1-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><ul style=\"list-style-type: none; margin-left: 1em; margin-top: 1em\">\n<li style=\"margin-bottom: 10px\"><span style=\"font-weight: 600\">Secant:<\/span> A line that touches two points on the circumference of the circle.<\/li>\n<li style=\"margin-bottom: 10px\"><span style=\"font-weight: 600\">Chord:<\/span> A line segment that joins two points on the circumference of the circle.<\/li>\n<li ><span style=\"font-weight: 600\">Tangent:<\/span> A line that touches the circle\u2019s circumference only once.<\/li>\n<\/ul>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-1-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-1-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #2:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the value of \\(x\\)?  <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Secant-chord-and-tangent-circle-example-2.svg\" alt=\"A circle with two intersecting lines forming an angle of x\u00b0 at the circumference and an external angle of 82\u00b0.\" width=\"318\" height=\"270\" class=\"aligncenter size-full wp-image-274789\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">82\u00b0<\/div><div class=\"PQ\"  id=\"PQ-2-2\">31\u00b0<\/div><div class=\"PQ\"  id=\"PQ-2-3\">42\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-4\">41\u00b0<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-2\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-2-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>In the figure, \\(x\\) is the measure of an inscribed angle. An inscribed angle is half of the intercepted arc.<\/p>\n<p>In this case, the intercepted arc is 82\u00b0. Half of 82\u00b0 is 41, so the inscribed angle is 41\u00b0.<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-2-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-2-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #3:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nWhat is the measure of the interior angle with a measure of \\(x\u00b0\\)?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Secant-chord-and-tangent-circle-example-1.svg\" alt=\"A circle with two intersecting secants; one angle outside the circle is labeled 92\u00b0, the other is 138\u00b0, and the angle inside the circle is marked as x\u00b0.\" width=\"330\" height=\"289\" class=\"aligncenter size-full wp-image-274786\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">125\u00b0<\/div><div class=\"PQ\"  id=\"PQ-3-2\">230\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">115\u00b0<\/div><div class=\"PQ\"  id=\"PQ-3-4\">46\u00b0<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-3\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-3-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The interior angle, \\(x\\), can be determined using the formula \\(x=\\frac{1}{2}(a\u00b0+b\u00b0)\\), where \\(a\\) and \\(b\\) are the intercepted arcs.  <\/p>\n<p style=\"text-align: center; line-height: 40px\">\n\\(x=\\frac{1}{2}(92\u00b0+138\u00b0)\\)<br \/>\n\\(x=\\frac{1}{2}(230\u00b0)\\)<br \/>\n\\(x=115\u00b0\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-3-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-3-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #4:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nA flashlight is shining out into the forest at \\(x\u00b0\\). The corresponding intercepted arcs formed by the shining light are 21\u00b0 and 162\u00b0. What is the angle of light being projected from the flashlight? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-4-1\">70.5\u00b0<\/div><div class=\"PQ\"  id=\"PQ-4-2\">114\u00b0<\/div><div class=\"PQ\"  id=\"PQ-4-3\">39\u00b0<\/div><div class=\"PQ\"  id=\"PQ-4-4\">74.5\u00b0<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-4\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-4-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The angle of \\(x\\) can be determined using the formula \\(x=\\frac{1}{2}(a\u00b0-b\u00b0)\\) where \\(a\\) and \\(b\\) represent the intercepted arcs. <\/p>\n<p style=\"text-align: center; line-height: 40px\">\n\\(x=\\frac{1}{2}(162\u00b0-21\u00b0)\\)<br \/>\n\\(x=\\frac{1}{2}(141\u00b0)\\)<br \/>\n\\(x=70.5\u00b0\\)\n<\/p>\n<p>The angle of light shining from the flashlight is 70.5\u00b0. <\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-4-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-4-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"PQ\">\n\t\t\t\t\t<strong>Question #5:<\/strong>\n\t\t\t\t\t<div style=\"margin-left:10px;\"><p>&nbsp;<br \/>\nYou are welding circular earrings to sell at your local farmers market. Each earring is circular with two bars through the circle. You want each earring to look the same, so you want to calculate the exact angle measure of the interior angle. The measure of the two arcs intercepted by the bars are 72\u00b0 and 70\u00b0, respectively. What is the measure of angle \\(x\\)? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">70\u00b0<\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">71\u00b0<\/div><div class=\"PQ\"  id=\"PQ-5-3\">72\u00b0<\/div><div class=\"PQ\"  id=\"PQ-5-4\">74\u00b0<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t<input id=\"PQ-5\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5\" style=\"width: 150px;\">Show Answer<\/label>\n\t\t\t\t\t<div class=\"answer\" id=\"PQ-5-spoiler\">\n\t\t\t\t\t\t<strong>Answer:<\/strong><div style=\"margin-left:10px;\"><p>The unknown angle is inside of the circle, so the angle \\(x\\) can be calculated using the formula \\(x=\\frac{1}{2}(a\u00b0+b\u00b0)\\), where \\(a\\) and \\(b\\) represent the intercepted arcs. <\/p>\n<p style=\"text-align: center; line-height: 40px\">\n\\(x=\\frac{1}{2}(72\u00b0+70\u00b0)\\)<br \/>\n\\(x=\\frac{1}{2}(142\u00b0)\\)<br \/>\n\\(x=71\u00b0\\)<\/p>\n<\/div>\n\t\t\t\t\t\t<input id=\"PQ-5-hide\" type=\"checkbox\" class=\"spoiler_button\" \/><label for=\"PQ-5-hide\" style=\"width: 150px;\">Hide Answer<\/label>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div><\/div>\n<\/div>\n\n<div class=\"home-buttons\">\n<p><a href=\"https:\/\/www.mometrix.com\/academy\/geometry\/\">Return to Geometry Videos<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Return to Geometry Videos<\/p>\n","protected":false},"author":1,"featured_media":100744,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":{"0":"post-89134","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-circle-video","7":"page_type-video","8":"content_type-practice-questions","9":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/89134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/comments?post=89134"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/89134\/revisions"}],"predecessor-version":[{"id":244120,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/89134\/revisions\/244120"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100744"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=89134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}