Question 3
The segment $\overline{AB}$ is a diameter of a circle with the centre $O$. On the circle the point $C$ is given such that $OC$ is perpendicular to $AB$. Let $P$ be a point on the shorter arc $\widehat{BC}$. The lines $CP$ and $AB$ intersect at the point $Q$, and the point $R$ is the intersection of the line $AP$ and the line through $Q$ perpendicular to the line $AB$.
Prove that $|BQ| = |QR|$. (Macedonia 2013)
Prove that $|BQ| = |QR|$. (Macedonia 2013)