2014 Canadian MO Problems/Problem 4

Problem

The quadrilateral $ABCD$ is inscribed in a circle. The point $P$ lies in the interior of $ABCD$ , and $\angle P AB = \angle P BC = \angle P CD = \angle P DA$ . The lines $AD$ and $BC$ meet at $Q$ , and the lines $AB$ and $CD$ meet at $R$ . Prove that the lines $PQ$ and $PR$ form the same angle as the diagonals of $ABCD$ .

Solution

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2014 Canadian MO Problems/Problem 4

Problem

Solution