MathDB

23

Part of 2013 Harvard-MIT Mathematics Tournament

Problems(1)

2013 HMMT Guts #23: Concurrent Lines in a Parallelogram

Source:

3/26/2013
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.
HMMTgeometryparallelogramratiotrigonometry