Question 180
Let $ABC$ be a triangle. Denote by $L, M, N$ the midpoints of $[BC]$, $[CA]$ and $[AB]$. Let $(d)$ be the tangent at $A$ to the circumcircle of $ABC$. The line $(LM)$ meets $(d)$ at $P$, and the line $(LN)$ meets $(d)$ at $Q$. Show that $(CP)$ and $(BQ)$ are parallel.