{"id":140,"date":"2023-01-18T21:23:41","date_gmt":"2023-01-18T21:23:41","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=140"},"modified":"2023-01-18T21:26:19","modified_gmt":"2023-01-18T21:26:19","slug":"a-second-problem-of-a-circles-in-a-quadrilateral","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2023\/01\/18\/a-second-problem-of-a-circles-in-a-quadrilateral\/","title":{"rendered":"A Second Problem of Circles in a Quadrilateral"},"content":{"rendered":"\n<p>As in the first problem a 30-60-90\u00b0 triangle is joined to a 45-90-45\u00b0 triangle, long side to short side to form a composite quadrilateral. In this new problem a circle is fitted lower in the diagram such that it is tangential to only the hypotenuse of the 45-90-45\u00b0 triangle and to two sides of 30-60-90\u00b0 triangle. What is the radius of the circle? Scale the diagram as convenient for your calculations. Which of these two problems has the bigger circle?<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"847\" height=\"1024\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045_alternate-847x1024.png\" alt=\"\" class=\"wp-image-141\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045_alternate-847x1024.png 847w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045_alternate-248x300.png 248w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045_alternate-768x928.png 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045_alternate-1271x1536.png 1271w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045_alternate-1695x2048.png 1695w\" sizes=\"auto, (max-width: 847px) 100vw, 847px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>As in the first problem a 30-60-90\u00b0 triangle is joined to a 45-90-45\u00b0 triangle, long side to short side to form a composite quadrilateral. In this&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,5],"tags":[13,12],"class_list":["post-140","post","type-post","status-publish","format-standard","hentry","category-geogebra","category-geometry","tag-geogebra","tag-geometry"],"_links":{"self":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/140","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=140"}],"version-history":[{"count":4,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/140\/revisions"}],"predecessor-version":[{"id":146,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/140\/revisions\/146"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=140"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=140"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=140"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}