Question 75
Let $ABC$ be a triangle in which $BC \lt AC$. Let $M$ be the mid-point of $AB$; $AP$ be the altitude from $A$ on to $BC$; and $BQ$ be the altitude from $B$ on to $AC$. Suppose $QP$ produced meets $AB$ (extended) in $T$. If $H$ is the ortho-centre of $ABC$, prove that $TH$ is perpendicular to $CM$.