{"id":475,"date":"2022-04-13T11:05:17","date_gmt":"2022-04-13T11:05:17","guid":{"rendered":"http:\/\/10thclass.deltapublications.in\/?page_id=475"},"modified":"2023-12-30T06:16:09","modified_gmt":"2023-12-30T06:16:09","slug":"aa-3-construct-a-regular-hexagon-inscribed-in-a-circle","status":"publish","type":"page","link":"https:\/\/10thclass.deltapublications.in\/index.php\/aa-3-construct-a-regular-hexagon-inscribed-in-a-circle\/","title":{"rendered":"AA.3 Construct a regular hexagon inscribed in a circle"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"> <strong>Construct a regular hexagon inscribed in a circle<\/strong><\/h2>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#f7d3d3\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-text-color has-link-color wp-elements-3b6eb5258c65d9752a1855623a1fa859\" style=\"color:#b00012\"><strong>The diagram below shows a nearly completed construction of a regular hexagon inscribed in \u2a00A with a vertex at B. Complete the construction.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"731\" height=\"530\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.0.png\" alt=\"\" class=\"wp-image-11258\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.0.png 731w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.0-300x218.png 300w\" sizes=\"auto, (max-width: 731px) 100vw, 731px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Part of the construction was done for you. Here are the steps to create this part of the construction.<br>Start with the objects in the diagram below.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"177\" height=\"191\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.1.png\" alt=\"\" class=\"wp-image-11293\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw a circle with radius AB centred at B.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"195\" height=\"250\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.2.png\" alt=\"\" class=\"wp-image-11294\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mark the points where \u2a00A and \u2a00B intersect. Call them C and D.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"279\" height=\"265\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.3.png\" alt=\"\" class=\"wp-image-11295\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Since A, C, and D are all on \u2a00B, AB=BC=BD. Since B, C, and D are all on \u2a00A, AB=AC=AD. This means that AB=AC=AD=BC=BD.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"273\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.4.png\" alt=\"\" class=\"wp-image-11296\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>So, \u25b3ABC and \u25b3ABD are congruent equilateral triangles.<\/li>\n\n\n\n<li>Draw the line through A and B.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"269\" height=\"314\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.5.png\" alt=\"\" class=\"wp-image-11297\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.5.png 269w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.5-257x300.png 257w\" sizes=\"auto, (max-width: 269px) 100vw, 269px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the line through A and C.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"289\" height=\"313\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.6.png\" alt=\"\" class=\"wp-image-11299\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.6.png 289w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.6-277x300.png 277w\" sizes=\"auto, (max-width: 289px) 100vw, 289px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the line through A and D.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"332\" height=\"324\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.7.png\" alt=\"\" class=\"wp-image-11291\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.7.png 332w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.7-300x293.png 300w\" sizes=\"auto, (max-width: 332px) 100vw, 332px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mark the point other than B where \u2a00A and AB intersect. Call it E.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"355\" height=\"321\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.8.png\" alt=\"\" class=\"wp-image-11289\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.8.png 355w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.8-300x271.png 300w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mark the point other than C where \u2a00A and AC intersect. Call it F.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"345\" height=\"335\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.9.png\" alt=\"\" class=\"wp-image-11288\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.9.png 345w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.9-300x291.png 300w\" sizes=\"auto, (max-width: 345px) 100vw, 345px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mark the point other than D where \u2a00A and AD intersect. Call it G.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"349\" height=\"345\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.10.png\" alt=\"\" class=\"wp-image-11287\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.10.png 349w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.10-300x297.png 300w\" sizes=\"auto, (max-width: 349px) 100vw, 349px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the segment between B and C.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"315\" height=\"344\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.11.png\" alt=\"\" class=\"wp-image-11284\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.11.png 315w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.11-275x300.png 275w\" sizes=\"auto, (max-width: 315px) 100vw, 315px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the segment between C and G.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"301\" height=\"345\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.12.png\" alt=\"\" class=\"wp-image-11283\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.12.png 301w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.12-262x300.png 262w\" sizes=\"auto, (max-width: 301px) 100vw, 301px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the segment between G and E.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"326\" height=\"352\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.13.png\" alt=\"\" class=\"wp-image-11282\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.13.png 326w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.13-278x300.png 278w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the segment between E and F.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"334\" height=\"336\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.14.png\" alt=\"\" class=\"wp-image-11281\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.14.png 334w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.14-298x300.png 298w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.14-150x150.png 150w\" sizes=\"auto, (max-width: 334px) 100vw, 334px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Draw the segment between F and D.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"298\" height=\"337\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.15.png\" alt=\"\" class=\"wp-image-11280\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.15.png 298w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.15-265x300.png 265w\" sizes=\"auto, (max-width: 298px) 100vw, 298px\" \/><\/figure>\n\n\n\n<p><strong>Complete the construction.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To complete the construction of a regular hexagon inscribed in \u2a00A with a vertex at B, carry out the following step:<\/li>\n\n\n\n<li>Draw the segment between B and D.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"322\" height=\"339\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.16.png\" alt=\"\" class=\"wp-image-11279\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.16.png 322w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.16-285x300.png 285w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"733\" height=\"54\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/56.png\" alt=\"\" class=\"wp-image-11270\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/56.png 733w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/56-300x22.png 300w\" sizes=\"auto, (max-width: 733px) 100vw, 733px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"328\" height=\"363\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.17.png\" alt=\"\" class=\"wp-image-11278\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.17.png 328w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.17-271x300.png 271w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/figure>\n\n\n\n<p>This means the six triangles formed by the segments between A and these six points are all isosceles.<br>Now, since \u25b3ABC and \u25b3ABD are equilateral triangles, m\u2220BAC and m\u2220BAD are both 60\u00b0. Find m\u2220CAG using the fact that these three angles form a straight angle.<br>m\u2220CAG   = 180\u00b0\u2013m\u2220BAC\u2013m\u2220BAD<br>= 180\u00b0\u201360\u00b0\u201360\u00b0<br>= 60\u00b0<br>By the vertical angle theorem, it follows that m\u2220EAG, m\u2220EAF, and m\u2220DAF are all 60\u00b0. An isosceles triangle containing a 60\u00b0 angle is equilateral, so \u25b3ABC, \u25b3ACG, \u25b3AEG, \u25b3AEF, \u25b3ADF and \u25b3ABD are all equilateral. Since each of these triangles has a side in common, they are all congruent equilateral triangles.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"401\" height=\"415\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.18.png\" alt=\"\" class=\"wp-image-11277\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.18.png 401w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/12\/3.18-290x300.png 290w\" sizes=\"auto, (max-width: 401px) 100vw, 401px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>So, all sides and interior angles of hexagon BCGEFD are congruent to each other. In other words, BCGEFD is a regular hexagon.<\/li>\n<\/ul>\n<\/div><\/div>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-d10c1106a03fa0d2c642217354ec023a\" style=\"color:#d90000\">Let&#8217;s practice!\ud83d\udd8a\ufe0f<\/p>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/65577\/589\/262\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-174.png\" alt=\"\" class=\"wp-image-7527\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-174.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-174-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-174-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-193.png\" alt=\"\" class=\"wp-image-7528\" srcset=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-193.png 500w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-193-300x300.png 300w, https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-193-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Construct a regular hexagon inscribed in a circle Learn with an example The diagram below shows a nearly completed construction of a regular hexagon inscribed in \u2a00A with a vertex at B. Complete the construction. Part of the construction was done for you. Here are the steps to create this part of the construction.Start with<a class=\"more-link\" href=\"https:\/\/10thclass.deltapublications.in\/index.php\/aa-3-construct-a-regular-hexagon-inscribed-in-a-circle\/\">Continue reading <span class=\"screen-reader-text\">&#8220;AA.3 Construct a regular hexagon inscribed in a circle&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-475","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/475","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=475"}],"version-history":[{"count":8,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/475\/revisions"}],"predecessor-version":[{"id":11302,"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/475\/revisions\/11302"}],"wp:attachment":[{"href":"https:\/\/10thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=475"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}