{"id":4404,"date":"2013-06-30T05:13:24","date_gmt":"2013-06-30T05:13:24","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4404"},"modified":"2026-03-25T10:50:43","modified_gmt":"2026-03-25T15:50:43","slug":"tangent-lines-from-a-point-outside-a-circle","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/tangent-lines-from-a-point-outside-a-circle\/","title":{"rendered":"Tangent Lines of a Circle"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_VMRtka56TrM\" 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_VMRtka56TrM\" data-source-videoID=\"VMRtka56TrM\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Tangent Lines of a Circle Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Tangent Lines of a Circle\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_VMRtka56TrM:hover {cursor:pointer;} img#videoThumbnailImage_VMRtka56TrM {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/1258-tangent-lines-of-a-circle-1.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_VMRtka56TrM\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_VMRtka56TrM\" 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\",\"Tangent Lines of a Circle\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_VMRtka56TrM\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_VMRtka56TrM\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_VMRtka56TrM\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction 1hI_Function() {\n  var x = document.getElementById(\"1hI\");\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=\"1hI_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=\"1hI\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#How_a_Line_and_a_Circle_Can_Interact\" class=\"smooth-scroll\">How a Line and a Circle Can Interact<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#When_a_Line_Misses_the_Circle_Entirely\" class=\"smooth-scroll\">When a Line Misses the Circle Entirely<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#When_a_Line_Just_Touches_the_Circle\" class=\"smooth-scroll\">When a Line Just Touches the Circle<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Finding_the_Slope_of_a_Tangent_Line\" class=\"smooth-scroll\">Finding the Slope of a Tangent Line<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Tangent_Line_of_a_Circle_Practice_Questions\" class=\"smooth-scroll\">Tangent Line of a Circle 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>Hi, and welcome to this video on tangent lines! <\/p>\n<p>Today we\u2019re going to explore what can happen when a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/the-diameter-radius-and-circumference-of-circles\/\">circle<\/a> and a line meet, and we\u2019ll start by exploring how these two shapes can interact.<\/p>\n<h2><span id=\"How_a_Line_and_a_Circle_Can_Interact\" class=\"m-toc-anchor\"><\/span>How a Line and a Circle Can Interact<\/h2>\n<p>\nThe most a line can intersect with a circle is by crossing over it, like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-115481 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Screen-Shot-2022-02-25-at-2.20.48-PM.png\" alt=\"Circle diagram labeled with secant and chord\" width=\"578\" height=\"366\" style=\"box-shadow: 1.5px 1.5px 3px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Screen-Shot-2022-02-25-at-2.20.48-PM.png 578w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Screen-Shot-2022-02-25-at-2.20.48-PM-300x190.png 300w\" sizes=\"auto, (max-width: 578px) 100vw, 578px\" \/><\/p>\n<p>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 that is called a <strong>chord<\/strong>. A line that cuts across a circle in this way is called a <strong>secant to the circle<\/strong>. <\/p>\n<h2><span id=\"When_a_Line_Misses_the_Circle_Entirely\" class=\"m-toc-anchor\"><\/span>When a Line Misses the Circle Entirely<\/h2>\n<p>\nAnother scenario would be a line that doesn\u2019t intersect the circle at all, like this:<\/p>\n<p>Even though the arrows on the line represent the line going on forever, it will never intersect with the circle. There really isn\u2019t much to say about this one, but we should be aware that it can happen.<\/p>\n<h2><span id=\"When_a_Line_Just_Touches_the_Circle\" class=\"m-toc-anchor\"><\/span>When a Line Just Touches the Circle<\/h2>\n<p>\nThere\u2019s one other thing that can happen with a circle and a line, and it looks like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-115475 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Screen-Shot-2022-02-25-at-2.21.03-PM.png\" alt=\"Circle diagram with a point of tangent\" width=\"557\" height=\"338\" style=\"box-shadow: 1.5px 1.5px 5px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Screen-Shot-2022-02-25-at-2.21.03-PM.png 557w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Screen-Shot-2022-02-25-at-2.21.03-PM-300x182.png 300w\" sizes=\"auto, (max-width: 557px) 100vw, 557px\" \/><\/p>\n<p>In this case, the line only touches the circle at one point. This line can be described as <strong>tangent to the circle<\/strong>, or <strong>tangential<\/strong>. The point where the line and the circle touch is called the <strong>point of tangency<\/strong>. <\/p>\n<p>Looking closely at our diagram we can see a radius of the circle meeting our tangential line at a 90-degree 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. We can see that with a close up that shows the angles that are just a few degrees away from 90 degrees: <\/p>\n<p>Even if the angle were even closer to 90 degrees, such as 90.1\u00b0 and 89.9\u00b0 this would still happen, though it would be harder to show in a diagram, at least without a microscope. <\/p>\n<h2><span id=\"Finding_the_Slope_of_a_Tangent_Line\" class=\"m-toc-anchor\"><\/span>Finding the Slope of a Tangent Line<\/h2>\n<p>\nNow, what if we\u2019re given a circle with a tangent line, and we want to know the <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/finding-the-slope-of-a-line\/\">slope of the line<\/a>? If we know the center of the circle and point of tangency then we can figure it out. Let\u2019s take a look:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-115478 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Screen-Shot-2022-02-25-at-2.23.14-PM.png\" alt=\"circle with a green line with points (0,0) and (-3,-5)\" width=\"377\" height=\"363\" style=\"box-shadow: 1.5px 1.5px 5px grey\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Screen-Shot-2022-02-25-at-2.23.14-PM.png 377w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2022\/02\/Screen-Shot-2022-02-25-at-2.23.14-PM-300x289.png 300w\" sizes=\"auto, (max-width: 377px) 100vw, 377px\" \/><\/p>\n<p>We can see that the center of the circle is at the origin, or the point (0,0), and the point of tangency is at (-3,-5). Since we have two points on the radius we can determine the slope of the radius using the slope formula:<\/p>\n<p>Let\u2019s call the center of the circle point #1 and the point of tangency point #2. <\/p>\n<p>Remember, it doesn\u2019t matter which point we call #1 or #2, just that we need to be consistent with how we substitute once we decide.<\/p>\n<p>So we\u2019ve found the slope of the radius! But that\u2019s not the final answer because we\u2019re trying to find the slope of the tangent line. Since the tangent line is perpendicular to the radius, we can find it by taking the negative reciprocal of the slope of the radius. Finding the <strong>negative reciprocal<\/strong> just means that we flip it over and change the sign. So the slope of the tangent line is -3\/5.<\/p>\n<p>That\u2019s all there is to it! Thanks for watching, and happy studying!<\/p>\n<ul class=\"citelist\">\n<li><a href=\"https:\/\/www.mathopenref.com\/tangentline.html\"target=\"_blank\">\u201cTangent to a Circle Definition &#8211; Math Open Reference.\u201d n.d.<\/a><\/li>\n<li><a href=\"https:\/\/www.varsitytutors.com\/act_math-help\/how-to-find-the-equation-of-a-tangent-line\"target=\"_blank\">\u201cHow to Find the Equation of a Tangent Line &#8211; ACT Math.\u201d n.d.<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Tangent_Line_of_a_Circle_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Tangent Line of a Circle 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 \/>\nIn the image below, a line crosses over a circle. The line intersects the circle at exactly two points, and creates a red line segment between those two points. What is this red line segment called?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-72091 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/circle-with-line-segment-passing-through-two-points-part-of-the-line-segment-that-is-between-the-two-points-is-highlighted-red.png\" alt=\"circle with line segment passing through two points, part of the line segment that is between the two points is highlighted red\" width=\"160\" height=\"156\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/circle-with-line-segment-passing-through-two-points-part-of-the-line-segment-that-is-between-the-two-points-is-highlighted-red.png 868w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/circle-with-line-segment-passing-through-two-points-part-of-the-line-segment-that-is-between-the-two-points-is-highlighted-red-300x293.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/circle-with-line-segment-passing-through-two-points-part-of-the-line-segment-that-is-between-the-two-points-is-highlighted-red-768x749.png 768w\" sizes=\"auto, (max-width: 160px) 100vw, 160px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">Diameter<\/div><div class=\"PQ\"  id=\"PQ-1-2\">Radius<\/div><div class=\"PQ\"  id=\"PQ-1-3\">Tangent<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">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;\"><p>A <strong>chord<\/strong> is a line segment that joins two points on the circumference of a circle.<\/p>\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 \/>\nPoint A is the center of the circle. Point C represents one point on the circumference of the circle. The blue line represents the radius of the circle. What is the term for the red line?<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2025\/10\/Circle-with-points-A-and-C.svg\" alt=\"A circle with center A, a radius AC, and a red tangent line touching the circle at point C, forming a right angle with the radius.\" width=\"265\" height=\"276\" class=\"aligncenter size-full wp-image-274318\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">Chord<\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-2\">Line of tangency<\/div><div class=\"PQ\"  id=\"PQ-2-3\">Slope line<\/div><div class=\"PQ\"  id=\"PQ-2-4\">Line of radius<\/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>A line that contacts the circumferences of a circle in exactly one location is called a line of tangency.<\/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 \/>\nFind the slope of the tangent line for a circle with a center point of \\((0,0)\\) and a point on the circumferences \\((4,5)\\).<\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">The slope of the tangent line is \\(-\\frac{5}{4}\\) <\/div><div class=\"PQ\"  id=\"PQ-3-2\">The slope of the tangent line is \\(\\frac{5}{4}\\) <\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-3\">The slope of the tangent line is \\(-\\frac{4}{5}\\) <\/div><div class=\"PQ\"  id=\"PQ-3-4\">The slope of the tangent line is \\(\\frac{4}{5}\\) <\/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>To find the slope of the tangent line, we first need to find the slope of the radius formed by connecting the center point \\((0,0)\\) to the point on the circumference \\((4,5)\\). This can be done using the slope formula:<\/p>\n<p style=\"text-align: center\">\\(m=\\dfrac{y_2-y_1}{x_2-x_1}\\)<\/p>\n<p>The formula now becomes \\(m=\\frac{5-0}{4-0}\\) which simplifies to \\(\\frac{5}{4}\\).<\/p>\n<p>The slope of the radius is \\(\\frac{5}{4}\\). The slope of the tangent line can be determined by finding the negative reciprocal of this. In other words, flip the fraction and change the sign. <\/p>\n<p>The negative reciprocal of \\(\\frac{5}{4}\\) is \\(-\\frac{4}{5}\\).<\/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 \/>\nFind the slope of the tangent line for a circle with a center point of \\((0,0)\\) and a point on the circumferences \\((5,1)\\). <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">The slope of the tangent line is \\(-\\frac{1}{4}\\) <\/div><div class=\"PQ\"  id=\"PQ-4-2\">The slope of the tangent line is \\(\\frac{1}{4}\\) <\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-3\">The slope of the tangent line is \\(-\\frac{5}{1}\\) <\/div><div class=\"PQ\"  id=\"PQ-4-4\">The slope of the tangent line is \\(\\frac{1}{5}\\) <\/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>To find the slope of the tangent line, we first need to find the slope of the radius formed by connecting the center point \\((0,0)\\) to the point on the circumference \\((5,1)\\). This can be done using the slope formula:<\/p>\n<p style=\"text-align: center\">\\(m=\\dfrac{y_2-y_1}{x_2-x_1}\\)<\/p>\n<p>The formula now becomes \\(m=\\frac{1-0}{5-0}\\) which simplifies to \\(\\frac{1}{5}\\). The slope of the radius is \\(\\frac{1}{5}\\). The slope of the tangent line can be determined by finding the negative reciprocal of this. In other words, flip the fraction and change the sign. <\/p>\n<p>The negative reciprocal of \\(\\frac{1}{5}\\) is \\(-\\frac{5}{1}\\). <\/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 \/>\nExplain why it is not possible to determine the slope of the tangent line in the example below.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\" wp-image-72088 aligncenter\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/black-circle-with-line-segment-extending-through-two-points-of-the-circle.png\" alt=\"black circle with line segment extending through two points of the circle\" width=\"162\" height=\"169\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/black-circle-with-line-segment-extending-through-two-points-of-the-circle.png 858w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/black-circle-with-line-segment-extending-through-two-points-of-the-circle-287x300.png 287w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/04\/black-circle-with-line-segment-extending-through-two-points-of-the-circle-768x803.png 768w\" sizes=\"auto, (max-width: 162px) 100vw, 162px\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-5-1\">The red line is not long enough to determine the slope of the tangent line. <\/div><div class=\"PQ correct_answer\"  id=\"PQ-5-2\">The red line is not tangential to the circle. A tangent line would cross the circle at exactly <em>one<\/em> point. <\/div><div class=\"PQ\"  id=\"PQ-5-3\">The red line needs to cut through the middle of the circle in order to determine the slope of the tangent line.<\/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 red line is not tangential to the circle because it intersects the circumference of the circle at more than one exact point. A line that intersects a circle in exactly two points is called a <strong>secant<\/strong>.<\/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":100351,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4404","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-circle-video","7":"page_category-math-advertising-group","8":"page_type-video","9":"content_type-practice-questions","10":"subject_matter-math"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4404","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=4404"}],"version-history":[{"count":5,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4404\/revisions"}],"predecessor-version":[{"id":261064,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4404\/revisions\/261064"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/100351"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=4404"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}