Question 48
From a point $P$ outside a circle centred at $O$, draw the two tangents to the circle touching it at $A, B$. Let $M$ be a point on the segment $AB$ and let $C, D$ be points on the circle with midpoint $M$. Let the tangents to the circle at $C, D$ intersect at $Q$. Show that $OQ \perp PQ$.