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2018 preRMO p5 computational with a tangential trapezium

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August 7, 2019
geometrytrapeziumtangentialincircletrapezoid

Problem Statement

Let ABCDABCD be a trapezium in which AB//CDAB //CD and AD⊥ABAD \perp AB. Suppose ABCDABCD has an incircle which touches ABAB at QQ and CDCD at PP. Given that PC=36PC = 36 and QB=49QB = 49, find PQPQ.
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