{"id":4482,"date":"2013-06-29T06:25:01","date_gmt":"2013-06-29T06:25:01","guid":{"rendered":"http:\/\/www.mometrix.com\/academy\/?page_id=4482"},"modified":"2026-03-26T11:57:58","modified_gmt":"2026-03-26T16:57:58","slug":"incenter-circumcenter-orthocenter-and-centroid","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/incenter-circumcenter-orthocenter-and-centroid\/","title":{"rendered":"Centroid, Incenter, Circumcenter, and Orthocenter"},"content":{"rendered":"\n\t\t\t<div id=\"mmDeferVideoEncompass_HnyNbywLpvI\" 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_HnyNbywLpvI\" data-source-videoID=\"HnyNbywLpvI\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/01\/circle-play-duotone.png\" alt=\"Centroid, Incenter, Circumcenter, and Orthocenter Video\" height=\"464\" width=\"825\" class=\"size-full\" data-matomo-title = \"Centroid, Incenter, Circumcenter, and Orthocenter\">\n\t\t\t<\/picture>\n\t\t\t<\/div>\n\t\t\t<style>img#videoThumbnailImage_HnyNbywLpvI:hover {cursor:pointer;} img#videoThumbnailImage_HnyNbywLpvI {background-size:contain;background-image:url(\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2023\/07\/updated-centroid-incenter-circumcenter-and-orthocenter-64c143b790d6b.webp\");}<\/style>\n\t\t\t<script defer>\n\t\t\t  jQuery(\"img#videoThumbnailImage_HnyNbywLpvI\").click(function() {\n\t\t\t\tlet videoId = jQuery(this).attr(\"data-source-videoID\");\n\t\t\t\tlet helpTag = '<div id=\"mmDeferVideoYTMessage_HnyNbywLpvI\" 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\",\"Centroid, Incenter, Circumcenter, and Orthocenter\");\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_HnyNbywLpvI\").html(tag);\n\t\t\t\tjQuery(\"div#mmDeferVideoEncompass_HnyNbywLpvI\").prepend(helpTag);\n\t\t\t\tsetTimeout(function(){jQuery(\"div#mmDeferVideoYTMessage_HnyNbywLpvI\").css(\"display\", \"block\");}, 2000);\n\t\t\t  });\n\t\t\t  \n\t\t\t<\/script>\n\t\t\n<p><script>\nfunction ZEI_Function() {\n  var x = document.getElementById(\"ZEI\");\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=\"ZEI_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=\"ZEI\" style=\"display:none;\">\n<ul>\n<li class=\"toc-h2\"><a href=\"#Incenter\" class=\"smooth-scroll\">Incenter<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Centroid\" class=\"smooth-scroll\">Centroid<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Centroid_1\" class=\"smooth-scroll\">Centroid<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Orthocenter\" class=\"smooth-scroll\">Orthocenter<\/a><\/li>\n<li class=\"toc-h2\"><a href=\"#Center_of_a_Triangle_Practice_Questions\" class=\"smooth-scroll\">Center of a Triangle 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>Where is the center of a triangle? How do you find it? It\u2019s not as easy as finding the center of a circle or a rectangle and for a very good reason\u2014there are as many as four different centers to a triangle, depending on how we try to find it! They are the incenter, centroid, circumcenter, and orthocenter.<\/p>\n<p>Today, we\u2019ll look at how to find each one.<\/p>\n<h2><span id=\"Incenter\" class=\"m-toc-anchor\"><\/span>Incenter<\/h2>\n<p>\nLet\u2019s start with the incenter. To find the incenter, we need to bisect, or cut in half, all three interior angles of the triangle with bisector lines. Let\u2019s take a look at a <a class=\"ylist\" href=\"https:\/\/www.mometrix.com\/academy\/introduction-to-types-of-triangles\/\">triangle<\/a> with the angle measures given.<\/p>\n<p>The angle on the left is 50 degrees, so we\u2019ll draw a line through it such that it\u2019s broken into two 25-degree angles. We\u2019ll do the same for the 60-degree angle on the right, yielding two 30-degree angles and the 70-degree angle on the top, creating two 35-degree angles, like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-70907\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/1.png\" alt=\"incenter of a triangle\" width=\"699\" height=\"686\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/1.png 699w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/1-300x294.png 300w\" sizes=\"auto, (max-width: 699px) 100vw, 699px\" \/> <\/p>\n<p>The point where the three angle bisector lines meet is the incenter.<\/p>\n<h2><span id=\"Centroid\" class=\"m-toc-anchor\"><\/span>Centroid<\/h2>\n<p>\nBut what if we don\u2019t cut the angles in half, but instead draw a line between each vertex and the midpoint of the line segment on the other side of the triangle? Let\u2019s take a look at another triangle but this time we can see the lengths of the sides instead of the angle measures.<\/p>\n<p>Let\u2019s start by drawing a line between the angle on the left in a way that will cut the opposite side in half. This is called a <strong>median of a triangle<\/strong>, and every triangle has three of them.<\/p>\n<p>As we can see, the opposite side that measures 10 meters has been split into two five-meter segments by our median. <\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-70910\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2.png\" alt=\"median line of a triangle\" width=\"752\" height=\"613\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2.png 874w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-300x244.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/2-768x626.png 768w\" sizes=\"auto, (max-width: 752px) 100vw, 752px\" \/> <\/p>\n<p>Now we need to draw the other two medians:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-70913\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/3.png\" alt=\"centroid of a triangle\" width=\"757\" height=\"609\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/3.png 823w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/3-300x241.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/3-768x618.png 768w\" sizes=\"auto, (max-width: 757px) 100vw, 757px\" \/> <\/p>\n<h2><span id=\"Centroid\" class=\"m-toc-anchor\"><\/span>Centroid<\/h2>\n<p>\nNow that we\u2019ve drawn all three medians, we can see where they intersect. This point is the centroid of the triangle and is our second type of triangle center.<\/p>\n<p>Now that we\u2019ve divided the angles in half to find the incenter and the sides in half to find the centroid, what other methods can we devise to find the other two centers? Remember, there\u2019s four!<\/p>\n<p>Let\u2019s try a variation of the last one. We\u2019ll start at the midpoint of each side again, but we\u2019ll draw our lines at a 90-degree angle from the side, like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-70916\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/4.png\" alt=\"perpendicular bisector of a triangle leg\" width=\"742\" height=\"584\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/4.png 871w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/4-300x236.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/4-768x605.png 768w\" sizes=\"auto, (max-width: 742px) 100vw, 742px\" \/> <\/p>\n<p>Notice that our line doesn\u2019t end up at an angle, or as we sometimes say, a vertex. It cuts through another side. That\u2019s totally fine! Let\u2019s do the same thing with the other two sides:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-70919\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/5.png\" alt=\"circumcenter of a triangle\" width=\"721\" height=\"599\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/5.png 821w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/5-300x249.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/5-768x638.png 768w\" sizes=\"auto, (max-width: 721px) 100vw, 721px\" \/>  <\/p>\n<p>As we can see, all of our sides have perpendicular bisectors and all three of our bisectors meet at a point. This point is called the <strong>circumcenter<\/strong> of the triangle.<\/p>\n<h2><span id=\"Orthocenter\" class=\"m-toc-anchor\"><\/span>Orthocenter<\/h2>\n<p>\nOnly one center left! For this one, let\u2019s keep our lines at 90 degrees, but move them so that they <em>do<\/em> end up at the three vertexes.<\/p>\n<p>When we do this, we\u2019re finding the <strong>altitudes<\/strong> of a triangle. You might remember altitude because we need it to find the area of a triangle. If we draw the other two we should find that they all meet again at a single point:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter  wp-image-70922\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/6.png\" alt=\"orthocenter of a triangle\" width=\"711\" height=\"600\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/6.png 848w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/6-300x253.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/6-768x648.png 768w\" sizes=\"auto, (max-width: 711px) 100vw, 711px\" \/><\/p>\n<p>This is our fourth and final triangle center, and it\u2019s called the <strong>orthocenter<\/strong>.<\/p>\n<p>So, do you think you can remember them all? Pause this video and try to match up the name of the center with the method for finding it:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-70925\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/7.png\" alt=\"practice question for centroid, incenter, circumcenter, and orthocenter\" width=\"1920\" height=\"1080\" srcset=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/7.png 1920w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/7-300x169.png 300w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/7-1024x576.png 1024w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/7-768x432.png 768w, https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2021\/03\/7-1536x864.png 1536w\" sizes=\"auto, (max-width: 1920px) 100vw, 1920px\" \/><\/p>\n<p>Thanks for watching, and happy studying!<\/p>\n<ul class=\"citelist\">\n<li><a href=\"https:\/\/www.mathopenref.com\/triangleincenter.html\"target=\"_blank\">\u201cTriangle Incenter, Description and Properties &#8211; Math Open Reference.\u201d<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"spoiler\" id=\"PQs-spoiler\">\n<h2 style=\"text-align:center\"><span id=\"Center_of_a_Triangle_Practice_Questions\" class=\"m-toc-anchor\"><\/span>Center of a Triangle 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 \/>\nThe center of the triangle below has been determined by constructing a line from each vertex to the opposite side in order to form a 90-degree angle with that side. This location is known as the ___________.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Triangle.Orthocenter.svg\" alt=\"A triangle with three altitude lines in red, each intersecting at a single point; right angles are marked at the bases of the altitudes.\" width=\"249.55\" height=\"200.1\" class=\"aligncenter size-full wp-image-287591\"  role=\"img\" \/><\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-1-1\">Incenter<\/div><div class=\"PQ\"  id=\"PQ-1-2\">Centroid<\/div><div class=\"PQ\"  id=\"PQ-1-3\">Circumcenter<\/div><div class=\"PQ correct_answer\"  id=\"PQ-1-4\">Orthocenter<\/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>The orthocenter of a triangle is determined by connecting a line from the vertex to the opposite side, so that a 90-degree angle is formed.<\/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 \/>\nThe center of a triangle can be determined by drawing perpendicular bisectors through the midpoint of each side length of a triangle. The center point where all three lines intersect is known as the __________. <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-2-1\">Incenter <\/div><div class=\"PQ\"  id=\"PQ-2-2\">Centroid <\/div><div class=\"PQ correct_answer\"  id=\"PQ-2-3\">Circumcenter <\/div><div class=\"PQ\"  id=\"PQ-2-4\">Orthocenter <\/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>The circumcenter of a triangle is located by drawing three perpendicular bisectors from the midpoint of each side length. The intersection point of all three lines is considered the circumcenter.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Triangle_Acute_Circumscribed.svg\" alt=\"A triangle inscribed in a red circle with its centroid marked as point O and medial triangle shown inside.\" width=\"248.4\" height=\"239.2\" class=\"aligncenter size-full wp-image-287597\"  role=\"img\" \/><\/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 \/>\nDetermine if the statement is true or false: <\/p>\n<div class=\"yellow-math-quote\">The circumcenter is located at the intersection point of three angle bisectors.<\/div>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-3-1\">True<\/div><div class=\"PQ correct_answer\"  id=\"PQ-3-2\">False<\/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 circumcenter is the point where three perpendicular bisectors intersect.<\/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 city planner is designing a triangular park. She plans to plant an oak tree in the center of the triangle. She decides to calculate the midpoint of each side length by measuring the total distance of each side and then dividing by two. From here, she draws a line from each midpoint to the opposite vertex. The point where all three lines intersect is where she plans to plant the tree.<\/p>\n<p>Which method did the city planner use to determine the center of the triangular park? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ\"  id=\"PQ-4-1\">Incenter<\/div><div class=\"PQ correct_answer\"  id=\"PQ-4-2\">Centroid<\/div><div class=\"PQ\"  id=\"PQ-4-3\">Circumcenter<\/div><div class=\"PQ\"  id=\"PQ-4-4\">Orthocenter<\/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 centroid is determined by connecting a line from the midpoint of each side length, to the opposite vertex. This is the method that the city planner used to determine where to plant the oak tree.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Triangle.Centroid.svg\" alt=\"A triangle with three intersecting red lines meeting at the center; sides are marked with single, double, and triple tick marks, and circles highlight key points.\" width=\"246.1\" height=\"198.95\" class=\"aligncenter size-full wp-image-287600\"  role=\"img\" \/><\/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 \/>\nMorgan is building a luxury A-frame cabin in the woods. She wants to determine the center of the triangular face of the cabin so that she can fit the pieces of glass in properly. Morgan wants to determine the middle of the triangle by bisecting each interior angle. She plans to create three angle bisectors that extend to the opposite side length of the triangle. Morgan will consider the point where all three lines intersect as the \u201ccenter\u201d of the triangle.<\/p>\n<p>Which method has Morgan used to determine the center of the triangle? <\/p>\n<\/div>\n\t\t\t\t\t<div class=\"PQ-Choices\"><div class=\"PQ correct_answer\"  id=\"PQ-5-1\">Incenter<\/div><div class=\"PQ\"  id=\"PQ-5-2\">Centroid<\/div><div class=\"PQ\"  id=\"PQ-5-3\">Circumcenter<\/div><div class=\"PQ\"  id=\"PQ-5-4\">Orthocenter<\/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 incenter of a triangle is found by creating three angle bisectors. The point where they intersect is the incenter. This is the strategy that Morgan chose in order to find the center of the triangular face of her A-frame cabin.<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/www.mometrix.com\/academy\/wp-content\/uploads\/2026\/02\/Incircle.svg\" alt=\"A triangle with its incircle and incenter shown; angle bisectors are marked in red, intersecting at the incenter, with the incircle touching all three sides.\" width=\"286.2\" height=\"197.55\" class=\"aligncenter size-full wp-image-287603\"  role=\"img\" \/><\/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":187097,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"","meta":{"footnotes":""},"class_list":{"0":"post-4482","1":"page","2":"type-page","3":"status-publish","4":"has-post-thumbnail","6":"page_category-math-advertising-group","7":"page_category-triangle-videos","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\/4482","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=4482"}],"version-history":[{"count":7,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4482\/revisions"}],"predecessor-version":[{"id":287594,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/pages\/4482\/revisions\/287594"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media\/187097"}],"wp:attachment":[{"href":"https:\/\/www.mometrix.com\/academy\/wp-json\/wp\/v2\/media?parent=4482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}