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.

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