Let A, B, C, and D be points on a circle such that AB = 22 and CD = 81. Point P is on segment AB with AP = 12, and Q is on segment CD with CQ = 6. The line through P and Q intersects the circle at X and Y. If PQ = 15, find XY.
Using power of a point on P and Q, we get that XY = XP + PQ + QY = 8 + 15 + 21 = 43.
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