# 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.

×