{"id":2560,"date":"2022-03-14T16:09:00","date_gmt":"2022-03-14T20:09:00","guid":{"rendered":"http:\/\/mathfun4kids.com\/mlog\/?p=2560"},"modified":"2024-10-25T12:31:47","modified_gmt":"2024-10-25T16:31:47","slug":"geometry-challenge-10","status":"publish","type":"post","link":"https:\/\/mathfun4kids.com\/mlog\/?p=2560","title":{"rendered":"Geometry Challenge &#8211; 10"},"content":{"rendered":"\n<p>In the diagram below, two congruent semi-circles that are tangent to each other, are inscribed inside a bigger semi-circle with its diameter as 10 unit. The area of the shaded region can be expressed as $\\dfrac{a}{b}\\pi$, where $a$ and $b$ are co-prime. Find the value of $a+b$.<\/p>\n\n\n\n<center>\n<svg width=\"230\" height=\"140\">\n<g transform=\"translate(20,0)\">\n<path d=\"M 0,120 A 100,100 1,0 1 200,120 L 0,120\" fill=\"lightgray\" stroke=\"black\"><\/path>\nstroke=&#8221;black&#8221; \/&gt;\n<path d=\"M 0,120 A 57.75 57.75 1,0, 1 115.5,120 L 0,120\" fill=\"white\" stroke=\"black\"><\/path>\n<g transform=\"translate(100, -57.5)\">\n<g transform=\"rotate(-135 57.75 120)\">\n<path d=\"M 0,120 A 57.75 57.75 1,0, 1 115.5,120 L 0,120\" fill=\"white\" stroke=\"black\"><\/path>\n<\/g>\n<\/g>\n\n<\/g>\n<\/svg>\n<\/center>\n","protected":false},"excerpt":{"rendered":"<p>In the diagram below, two congruent semi-circles that are tangent to each other, are inscribed inside a bigger semi-circle with its diameter as 10 unit. The area of the shaded region can be expressed as $\\dfrac{a}{b}\\pi$, where $a$ and $b$ &hellip; <a href=\"https:\/\/mathfun4kids.com\/mlog\/?p=2560\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[9],"tags":[],"_links":{"self":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/2560"}],"collection":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2560"}],"version-history":[{"count":2,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/2560\/revisions"}],"predecessor-version":[{"id":2614,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=\/wp\/v2\/posts\/2560\/revisions\/2614"}],"wp:attachment":[{"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2560"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2560"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathfun4kids.com\/mlog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2560"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}