{"id":81,"date":"2022-04-11T21:06:34","date_gmt":"2022-04-11T21:06:34","guid":{"rendered":"https:\/\/convexabacus.xyz\/?p=81"},"modified":"2022-04-11T21:07:10","modified_gmt":"2022-04-11T21:07:10","slug":"two-unit-squares-in-a-semicircle","status":"publish","type":"post","link":"https:\/\/convexabacus.xyz\/index.php\/2022\/04\/11\/two-unit-squares-in-a-semicircle\/","title":{"rendered":"Two Unit Squares in a Semicircle"},"content":{"rendered":"\n<p>Two unit squares are jammed inside a semicircle. The left square, whose base lies on the diameter, has a single vertex touching the circle. The right square, tilted 45 degrees such that one diagonal is perpendicular with the diameter has a vertex touching the diameter, a vertex touching the left square and two vertices touching the circle. Can you find an exact expression for the radius of the circle ?<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"583\" src=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/two-unit-squares-in-semicircle-1024x583.png\" alt=\"\" class=\"wp-image-82\" srcset=\"https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/two-unit-squares-in-semicircle-1024x583.png 1024w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/two-unit-squares-in-semicircle-300x171.png 300w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/two-unit-squares-in-semicircle-768x438.png 768w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/two-unit-squares-in-semicircle-1536x875.png 1536w, https:\/\/convexabacus.xyz\/wp-content\/uploads\/2022\/04\/two-unit-squares-in-semicircle-2048x1167.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption>Two unit squares in a semicircle, one tilted 45 degrees<\/figcaption><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Two unit squares are jammed inside a semicircle. The left square, whose base lies on the diameter, has a single vertex touching the circle. The right&#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":[5],"tags":[],"class_list":["post-81","post","type-post","status-publish","format-standard","hentry","category-geometry"],"_links":{"self":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/81","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=81"}],"version-history":[{"count":1,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/81\/revisions"}],"predecessor-version":[{"id":83,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/posts\/81\/revisions\/83"}],"wp:attachment":[{"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=81"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=81"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/convexabacus.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=81"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}