{"id":149,"date":"2023-01-18T21:46:26","date_gmt":"2023-01-18T21:46:26","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=149"},"modified":"2023-01-18T21:46:26","modified_gmt":"2023-01-18T21:46:26","slug":"a-fourth-problem-of-circles-in-a-quadrilateral","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2023\/01\/18\/a-fourth-problem-of-circles-in-a-quadrilateral\/","title":{"rendered":"A Fourth Problem of Circles in a Quadrilateral"},"content":{"rendered":"\n<p>As in the three preceding 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 side by side 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<p>The first of these four problems was posted here <a href=\"https:\/\/convexabacus.xyz\/index.php\/2023\/01\/15\/a-formula-for-generating-some-geometry-problems\/\" data-type=\"URL\" data-id=\"https:\/\/convexabacus.xyz\/index.php\/2023\/01\/15\/a-formula-for-generating-some-geometry-problems\/\">https:\/\/convexabacus.xyz\/index.php\/2023\/01\/15\/a-formula-for-generating-some-geometry-problems\/<\/a><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"888\" height=\"1024\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/horizontal_circles_in_quadrilateral-888x1024.png\" alt=\"\" class=\"wp-image-150\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/horizontal_circles_in_quadrilateral-888x1024.png 888w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/horizontal_circles_in_quadrilateral-260x300.png 260w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/horizontal_circles_in_quadrilateral-768x886.png 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/horizontal_circles_in_quadrilateral-1331x1536.png 1331w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/horizontal_circles_in_quadrilateral-1775x2048.png 1775w\" sizes=\"auto, (max-width: 888px) 100vw, 888px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>As in the three preceding 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&#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-149","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\/149","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=149"}],"version-history":[{"count":1,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/149\/revisions"}],"predecessor-version":[{"id":151,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/149\/revisions\/151"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=149"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}