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2013 HMMT Guts #23: Concurrent Lines in a Parallelogram

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March 26, 2013
HMMTgeometryparallelogramratiotrigonometry

Problem Statement

Let ABCDABCD be a parallelogram with AB=8AB=8, AD=11AD=11, and ∠BAD=60∘\angle BAD=60^\circ. Let XX be on segment CDCD with CX/XD=1/3CX/XD=1/3 and YY be on segment ADAD with AY/YD=1/2AY/YD=1/2. Let ZZ be on segment ABAB such that AXAX, BYBY, and DZDZ are concurrent. Determine the area of triangle XYZXYZ.
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