Problem

Source: ELMO Shortlist 2010, G2

Tags: geometry, parallelogram, trapezoid, geometry proposed



Given a triangle $ABC$, a point $P$ is chosen on side $BC$. Points $M$ and $N$ lie on sides $AB$ and $AC$, respectively, such that $MP \parallel AC$ and $NP \parallel AB$. Point $P$ is reflected across $MN$ to point $Q$. Show that triangle $QMB$ is similar to triangle $CNQ$. Brian Hamrick.