{"id":137,"date":"2023-01-15T21:31:45","date_gmt":"2023-01-15T21:31:45","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=137"},"modified":"2023-01-18T21:56:24","modified_gmt":"2023-01-18T21:56:24","slug":"a-formula-for-generating-some-geometry-problems","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2023\/01\/15\/a-formula-for-generating-some-geometry-problems\/","title":{"rendered":"A Formula for Generating some Geometry Problems"},"content":{"rendered":"\n<p>I seem to have stumbled on a formula for generating some\u00a0geometry problems.<\/p>\n\n\n\n<p>(i) Combine two familiar shapes to create a composite irregular polygon.<\/p>\n\n\n\n<p>(ii) Fit one or two circles inside the construction.<\/p>\n\n\n\n<p>(iii) Adjust the shapes to fit precisely.<\/p>\n\n\n\n<p>In this problem a quadrilateral is composed of a 30-60-90\u00b0 triangle abutting a 45-90-45\u00b0 triangle, long side to short side. A circle is fitted that is tangential to two sides of the 45-90-45\u00b0 triangle and to the short side of 30-60-90\u00b0 triangle. What is the radius of the circle? Scale the diagram as convenient for your calculations. This is the first of a series of four problems.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"860\" height=\"1024\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045-860x1024.png\" alt=\"\" class=\"wp-image-138\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045-860x1024.png 860w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045-252x300.png 252w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045-768x914.png 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045-1290x1536.png 1290w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2023\/01\/circle_in_triangles_306090_459045-1720x2048.png 1720w\" sizes=\"auto, (max-width: 860px) 100vw, 860px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>I seem to have stumbled on a formula for generating some\u00a0geometry problems. (i) Combine two familiar shapes to create a composite irregular polygon. (ii) Fit one&#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-137","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\/137","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=137"}],"version-history":[{"count":1,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/137\/revisions"}],"predecessor-version":[{"id":139,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/137\/revisions\/139"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=137"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=137"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}