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P_1X bisects <Q_1P_1Q_2, start with concentric circles

Source: Canadian Junior Mathematical Olympiad - CJMO 2021 p1

May 29, 2021
geometryconcentricangle bisector

Problem Statement

Let C1C_1 and C2C_2 be two concentric circles with C1C_1 inside C2C_2. Let P1P_1 and P2P_2 be two points on C1C_1 that are not diametrically opposite. Extend the segment P1P2P_1P_2 past P2P_2 until it meets the circle C2C_2 in Q2Q_2. The tangent to C2C_2 at Q2Q_2 and the tangent to C1C_1 at P1P_1 meet in a point XX. Draw from X the second tangent to C2C_2 which meets C2C_2 at the point Q1Q_1. Show that P1XP_1X bisects angle Q1P1Q2Q_1P_1Q_2.
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