{"id":762,"date":"2016-07-30T07:22:20","date_gmt":"2016-07-30T12:22:20","guid":{"rendered":"https:\/\/trigonography.com\/?p=762"},"modified":"2022-06-25T01:30:45","modified_gmt":"2022-06-25T06:30:45","slug":"two-circles-puzzle","status":"publish","type":"post","link":"https:\/\/trigonography.com\/?p=762","title":{"rendered":"Two Circles Puzzle"},"content":{"rendered":"\n<p class=\"has-text-align-center wp-block-paragraph\" style=\"font-size:16px\">A puzzle by way of the <a href=\"http:\/\/math.stackexchange.com\/q\/1874736\/409\">Mathematics Stack Exchange<\/a> and\/or <a href=\"https:\/\/www.quora.com\/What-is-the-area-of-the-shaded-part\">Quora<\/a>. (Know the original source? <a href=\"mailto:trig@trigonography.com?subject=Two Circles Puzzle post\">Tell me!<\/a>)<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><a href=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/07\/trigonograph-circleareapuzzleA.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/07\/trigonograph-circleareapuzzleA.png\" alt=\"trigonograph-circleareapuzzleA\" width=\"720\" height=\"384\"\/><\/a><\/figure>\n<\/div>\n\n\n<div class=\"eqn-box\" style=\"margin-bottom: 20pt; font-size:12pt\">$$\\text{shaded area} \\;=\\; \\text{???}$$<\/div>\n\n\n\n<div style=\"padding-top: 128px; padding-bottom: 512px; font-size:12pt;\"><b>SPOILERS<\/b><\/div>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter\"><a href=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/07\/trigonograph-circleareapuzzleB.png\"><img decoding=\"async\" src=\"https:\/\/trigonography.com\/blog\/wp-content\/uploads\/2016\/07\/trigonograph-circleareapuzzleB.png\" alt=\"trigonograph-circleareapuzzleB\"\/><\/a><\/figure>\n<\/div>\n\n\n<p class=\"has-text-align-center wp-block-paragraph\" style=\"font-size:16px\">$$\\begin{align}3u + v &amp;= 3u \\;+\\; |OPST| \\;-\\; |\\text{sector}\\;OPT| \\\\[6pt]<br>&amp;= 3u \\;+\\; \\frac{3}{5}\\;|\\triangle SRT| \\;-\\; |\\text{sector}\\;OPT| \\\\[6pt]<br>&amp;= 3\\cdot \\frac{1}{4}r^2\\left( 4-\\pi \\right) \\;+\\;\\frac{3}{5}\\cdot r^2 \\;-\\; \\frac{1}{2}r^2 \\cdot 2\\theta<br>\\end{align}$$<\/p>\n\n\n\n<div class=\"eqn-box\" style=\"margin-bottom: 20pt; font-size:12pt;\">$$\\text{shaded area} \\;=\\; r^2\\left(\\;\\frac{18}{5} \\;-\\; \\frac{3}{4}\\pi \\;-\\; \\operatorname{atan}\\frac{1}{2}\\;\\right)$$<\/div>\n","protected":false},"excerpt":{"rendered":"<p>A puzzle by way of the Mathematics Stack Exchange and\/or Quora. (Know the original source? Tell me!) $$\\text{shaded area} \\;=\\; \\text{???}$$ SPOILERS $$\\begin{align}3u + v &amp;= 3u \\;+\\; |OPST| \\;-\\; |\\text{sector}\\;OPT| \\\\[6pt]&amp;= 3u \\;+\\; \\frac{3}{5}\\;|\\triangle SRT| \\;-\\; |\\text{sector}\\;OPT| \\\\[6pt]&amp;= 3\\cdot \\frac{1}{4}r^2\\left( 4-\\pi \\right) \\;+\\;\\frac{3}{5}\\cdot r^2 \\;-\\; \\frac{1}{2}r^2 \\cdot 2\\theta\\end{align}$$ $$\\text{shaded area} \\;=\\; r^2\\left(\\;\\frac{18}{5} \\;-\\; \\frac{3}{4}\\pi [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-762","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/762","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=762"}],"version-history":[{"count":10,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/762\/revisions"}],"predecessor-version":[{"id":1195,"href":"https:\/\/trigonography.com\/index.php?rest_route=\/wp\/v2\/posts\/762\/revisions\/1195"}],"wp:attachment":[{"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=762"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=762"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/trigonography.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=762"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}