CEMC Euclid, 2010

Combinatorics Difficulty 3.0 AMC 10/12 Prove it Canada

In the diagram, points $B$ , $P$ , $Q$ , and $C$ lie on line segment $AD$ . The semi-circle with diameter $AC$ has centre $P$ and the semi-circle with diameter $BD$ has centre $Q$ . The two semi-circles intersect at $R$ . If $\angle PRQ = 40^\circ$ , determine the measure of $\angle ARD$ .

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