Day 3: Inverted Thinking

Geometry Level 5

Let $O$ be the centre of a circle and let $P$ be a point inside this circle. Draw the radius $OQ$ such that $\angle OPQ$ is a right angle. Let $R$ be the intersection of the line $OP$ and of the tangent at $Q$ . Let $AB$ be a chord passing through $P$ of the circle.

Given that $\angle AOB = 150^{\circ}$ , find the value of $\angle ARP$ .

This problem is part of the set Advent Calendar 2014.