{"id":2822,"date":"2022-08-06T08:40:03","date_gmt":"2022-08-06T12:40:03","guid":{"rendered":"https:\/\/josmfs.net\/?p=2822"},"modified":"2024-04-06T12:54:56","modified_gmt":"2024-04-06T16:54:56","slug":"two-and-a-half-circles","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2022\/08\/06\/two-and-a-half-circles\/","title":{"rendered":"Two and a Half Circles"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-2820\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/08\/Two-and-a-Half-Circles-Fig2.jpg\" alt=\"\" width=\"250\" height=\"127\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/08\/Two-and-a-Half-Circles-Fig2.jpg 508w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/08\/Two-and-a-Half-Circles-Fig2-300x152.jpg 300w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/>Here is a problem from the 2022 Math Calendar.<\/p>\n<p>\u201cTwo small circles of radius 4 are inscribed in a large semicircle as shown.\u00a0 Find the radius of the large semicircle.\u201d<\/p>\n<p>As before, recall that all the answers are integer days of the month.<\/p>\n<p>As seemed to be implied by the original Math Calendar diagram, I made explicit that the upper circle was tangent to the midpoint of the chord.\u00a0 Otherwise, the problem is insufficiently constrained.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Two-and-a-Half-Circles-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2022\/08\/Two-and-a-Half-Circles-220803.pdf\">Two and a Half Circles<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a problem from the 2022 Math Calendar. \u201cTwo small circles of radius 4 are inscribed in a large semicircle as shown.\u00a0 Find the radius of the large semicircle.\u201d As before, recall that all the answers are integer days of the month. As seemed to be implied by the original Math Calendar diagram, I [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[183,13],"class_list":["post-2822","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-math-calendar","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2822","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=2822"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2822\/revisions"}],"predecessor-version":[{"id":3607,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/2822\/revisions\/3607"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=2822"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=2822"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=2822"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}