{"id":3367,"date":"2023-11-04T12:06:54","date_gmt":"2023-11-04T16:06:54","guid":{"rendered":"https:\/\/josmfs.net\/?p=3367"},"modified":"2024-04-05T11:01:59","modified_gmt":"2024-04-05T15:01:59","slug":"elliptic-circles","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2023\/11\/04\/elliptic-circles\/","title":{"rendered":"Elliptic Circles"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-3365\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/11\/Elliptic-Circles-Fig2.jpg\" alt=\"\" width=\"200\" height=\"212\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/11\/Elliptic-Circles-Fig2.jpg 400w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/11\/Elliptic-Circles-Fig2-284x300.jpg 284w\" sizes=\"auto, (max-width: 200px) 100vw, 200px\" \/>Here is another UKMT Senior Challenge problem for 2017.<\/p>\n<p>\u201cThe diagram shows a square PQRS with edges of length 1, and four arcs, each of which is a quarter of a circle. Arc TRU has centre P; arc VPW has centre R; arc UV has centre S; and arc WT has centre Q.<\/p>\n<p>What is the length of the perimeter of the shaded region?<\/p>\n<p style=\"text-align: center;\">A<span style=\"color: #ffffff;\">_<\/span>6<span style=\"color: #ffffff;\">___<\/span>B<span style=\"color: #ffffff;\">_<\/span>(2\u221a2 \u2013 1)\u03c0<span style=\"color: #ffffff;\">___<\/span>C<span style=\"color: #ffffff;\">_<\/span>(\u221a2 \u2013 <sup>1<\/sup>\/<sub>2<\/sub>)\u03c0<span style=\"color: #ffffff;\"> ___<\/span>D<span style=\"color: #ffffff;\">_<\/span>2<span style=\"color: #ffffff;\">___<\/span>E<span style=\"color: #ffffff;\">_<\/span>(3\u221a2 \u2013 2)\u03c0\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Elliptic-Circles-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2023\/11\/Elliptic-Circles-190902.pdf\">Elliptic Circles<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another UKMT Senior Challenge problem for 2017. \u201cThe diagram shows a square PQRS with edges of length 1, and four arcs, each of which is a quarter of a circle. Arc TRU has centre P; arc VPW has centre R; arc UV has centre S; and arc WT has centre Q. What is [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[40,83],"class_list":["post-3367","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-analytic-geometry","tag-ukmt-challenge"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3367","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=3367"}],"version-history":[{"count":2,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3367\/revisions"}],"predecessor-version":[{"id":3516,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/3367\/revisions\/3516"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=3367"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=3367"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=3367"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}