{"id":145,"date":"2023-01-18T21:38:10","date_gmt":"2023-01-18T21:38:10","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=145"},"modified":"2023-01-18T21:49:39","modified_gmt":"2023-01-18T21:49:39","slug":"a-third-problem-of-circles-in-a-quadrilateral","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2023\/01\/18\/a-third-problem-of-circles-in-a-quadrilateral\/","title":{"rendered":"A Third Problem of Circles in a Quadrilateral"},"content":{"rendered":"\n<p>As in the preceeding problems 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. Two congruent circles are fitted that are each tangential to two sides of the quadrilateral and are tangential to each other. The diagram is shown with the 45\u00b0 angle at the top and the right angle at the bottom. The circles are above and below each other in the diagram and fit precisely. What is the radius of the circles? Scale the diagram as convenient for your calculations.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"849\" height=\"1024\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/equal_circle_in_triangles_306090_459045-849x1024.png\" alt=\"\" class=\"wp-image-147\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/equal_circle_in_triangles_306090_459045-849x1024.png 849w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/equal_circle_in_triangles_306090_459045-249x300.png 249w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/equal_circle_in_triangles_306090_459045-768x926.png 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/equal_circle_in_triangles_306090_459045-1274x1536.png 1274w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/equal_circle_in_triangles_306090_459045-1699x2048.png 1699w\" sizes=\"auto, (max-width: 849px) 100vw, 849px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>As in the preceeding problems 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. Two congruent&#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-145","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\/145","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=145"}],"version-history":[{"count":3,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/145\/revisions"}],"predecessor-version":[{"id":153,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/145\/revisions\/153"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=145"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=145"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=145"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}