AUSTRIAN-POLISH 2002 Problem 1

Given a circle $G$ with center $O$ and radius $r$ . Let $AB$ be a fixed diameter of $G$ . Let $K$ be a fixed point of segment $AO$ . Denote by $t$ the line tangent to at $A$ . For any chord $CD$ (other than $AB$ ) passing through $K$ . Let $P$ and $Q$ be the points of intersection of lines $BC$ and $BD$ with $t$ . Prove that the product $AP\cdot AQ$ remains costant as the chord $CD$ varies.

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