Problem Solving (PS) | Re: The circle above has radius 8, and AD is parallel to BC. If the length

Circumference = 2πr = 2*π*8 = 16π

Arc CD:
Since inscribed angle CAD that intercepts arc CD = 45 degrees, the central angle that intercepts arc CD = 90 degrees, implying that arc CD consititutes 1/4 of the circumference:
1/4 * 16π = 4π

Arc AB:
Since line segments AD and BC are parallel, arcs AB and CD are equal in length.
Thus:
arc AB = 4π

Arc BXC:
Since arcs CD and AB together constitute 8π of the circumference, arcs BXC and AYD must consitute the remaining 8π.
Since BXC:AYD = 1:2 -- a ratio that has 3 parts, 1 of the 3 parts attiributed to arc BXC, the other 2 parts attritubed to arc AYD -- arc BXC must consitute 1/3 of the remaining 8π:
1/3 * 8π =\(\frac{8π}{3}\)

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Statistics : Posted by GMATGuruNY • on 01 May 2018, 06:06 • Replies 9 • Views 7817

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