Day 3: Inverted Thinking

Geometry Level 5

Let OO be the centre of a circle and let PP be a point inside this circle. Draw the radius OQOQ such that OPQ\angle OPQ is a right angle. Let RR be the intersection of the line OPOP and of the tangent at QQ. Let ABAB be a chord passing through PP of the circle.

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

This problem is part of the set Advent Calendar 2014.

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