CMO 2003 Problem 1

Let $I$ and $H$ be the incentre and orthocentre of triangle $ABC$ respectively. Let $P,Q$ be the midpoints of $AB,AC$ . The rays $PI,QI$ intersect $AC,AB$ at $R,S$ respectively. Suppose that $T$ is the circumcentre of triangle $BHC$ . Let $RS$ intersect $BC$ at $K$ . Prove that $A,I$ and $T$ are collinear if and only if $[BKS]=[CKR]$ .

Shen Wunxuan