Question 140
Let $P$, $Q$, and $R$ be the points on sides $BC$, $CA$, and $AB$ of an acute triangle $ABC$ such that triangle $PQR$ is equilateral and has minimal area among all such equilateral triangles. Prove that the perpendiculars from $A$ to line $QR$, from $B$ to line $RP$, and from $C$ to line $PQ$ are concurrent.