Question 13
Let $ABC$ be an acute triangle, with $AB \neq AC$. Let $D$ be the midpoint of $BC$ and $I, J, K$ be the feet of the altitudes from $A, B$ and $C$, respectively, in the triangle $ABC$. The perpendicular from $A$ to the line $AD$ meets the lines $BJ$ and $CK$ at points $N$ and $Q$, respectively, and the parallel to $BC$ through $A$ intersects the lines $IJ$ and $IK$ at $M$ and $P$, respectively. Prove that $MNPQ$ is a parallelogram.
Petru Braica
Petru Braica