{"id":1611,"date":"2020-05-16T08:25:53","date_gmt":"2020-05-16T12:25:53","guid":{"rendered":"http:\/\/josmfs.net\/?p=1611"},"modified":"2024-04-08T19:17:22","modified_gmt":"2024-04-08T23:17:22","slug":"lopsided-hexagon-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/05\/16\/lopsided-hexagon-problem\/","title":{"rendered":"Lopsided Hexagon Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1609\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/05\/Lopsided-Hexagon-Fig.jpg\" alt=\"\" width=\"200\" height=\"200\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/05\/Lopsided-Hexagon-Fig.jpg 200w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/05\/Lopsided-Hexagon-Fig-150x150.jpg 150w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>Here is another good problem from <em>Five Hundred Mathematical Challenges<\/em>:<\/p>\n<p><strong>\u201cProblem 100.<\/strong>\u00a0 A hexagon inscribed in a circle has three consecutive sides of length <em>a<\/em> and three consecutive sides of length <em>b<\/em>. Determine the radius of the circle.\u201d<\/p>\n<p>This problem made me think of the <a href=\"https:\/\/josmfs.net\/wordpress\/2019\/04\/04\/putnam-octagon-problem\/\">Putnam Octagon Problem<\/a>.\u00a0 Again my approach might be considered a bit pedestrian.\u00a0 500 Math Challenges had a slightly slicker solution.<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Lop-sided-Hexagon-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/05\/Lopsided-Hexagon-Problem-191126.pdf\">Lop-sided Hexagon Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another good problem from Five Hundred Mathematical Challenges: \u201cProblem 100.\u00a0 A hexagon inscribed in a circle has three consecutive sides of length a and three consecutive sides of length b. Determine the radius of the circle.\u201d This problem made me think of the Putnam Octagon Problem.\u00a0 Again my approach might be considered a [&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":[177,40,41],"class_list":["post-1611","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-500-math-challenges","tag-analytic-geometry","tag-trigonometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1611","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=1611"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1611\/revisions"}],"predecessor-version":[{"id":3756,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1611\/revisions\/3756"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1611"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1611"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1611"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}