MathDB
2011 PUMaC Geometry B3

Source:

September 24, 2019
geometry

Problem Statement

Let ABCDABCD be a trapezoid with ADAD parallel to BCBC, AD=2AD = 2, and BC=1BC = 1. Let MM be the midpoint of ADAD, and let PP be the intersection of BDBD with CMCM. Extend APAP to meet segment CDCD at point QQ. If the ratio CQ/QD=a/bCQ/QD = a/b, where aa and bb are positive integers and gcd(a,b)=1\text{gcd}(a, b) = 1, find a+ba + b.
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