{"id":4137,"date":"2024-10-19T13:59:26","date_gmt":"2024-10-19T17:59:26","guid":{"rendered":"https:\/\/josmfs.net\/?p=4137"},"modified":"2024-10-19T14:04:50","modified_gmt":"2024-10-19T18:04:50","slug":"another-octagonal-area-problem","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2024\/10\/19\/another-octagonal-area-problem\/","title":{"rendered":"Another Octagonal Area Problem"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-4134\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/10\/Another-Octagonal-Area-Fig2.jpg\" alt=\"\" width=\"200\" height=\"199\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/10\/Another-Octagonal-Area-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/10\/Another-Octagonal-Area-Fig2-300x300.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/10\/Another-Octagonal-Area-Fig2-150x150.jpg 150w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>This is a fairly straight-forward problem from the 1999 AIME problems.<\/p>\n<p>\u201cThe two squares shown share the same center O and have sides of length 1. The length of AB is 43\/99 and the area of octagon ABCDEFGH is m\/n where m and n are relatively prime positive integers. Find m + n.\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/10\/Another-Octagonal-Area-Answer.jpg\">Answer<\/a><\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/10\/Another-Octagonal-Area-Problem-240619.pdf\">Another Octagonal Area Problem<\/a> for solutions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is a fairly straight-forward problem from the 1999 AIME problems. \u201cThe two squares shown share the same center O and have sides of length 1. The length of AB is 43\/99 and the area of octagon ABCDEFGH is m\/n where m and n are relatively prime positive integers. Find m + n.\u201d Answer See [&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":[238,13],"class_list":["post-4137","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-aime","tag-plane-geometry"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4137","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=4137"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4137\/revisions"}],"predecessor-version":[{"id":4141,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/4137\/revisions\/4141"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=4137"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=4137"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=4137"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}