Question 75
Let $ABC$ be a triangle. On the lines $BC$, $CA$, respectively $AB$ the points $M$ and $N$, $P$ and $Q$, respectively $R$ and $S$ are taken, outside of the triangle, so that $MB = BS = AC$, $CP = CN = AB$ and $AR = AQ = BC$. Prove that the points $M, N, P, Q, R$ and $S$ are concyclic.