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Geometry tangent circles

Source: EGMO 2016 Day 2 Problem 4

April 13, 2016
geometryEGMOCharles LeytemEGMO 2016circles

Problem Statement

Two circles ω1\omega_1 and ω2\omega_2, of equal radius intersect at different points X1X_1 and X2X_2. Consider a circle ω\omega externally tangent to ω1\omega_1 at T1T_1 and internally tangent to ω2\omega_2 at point T2T_2. Prove that lines X1T1X_1T_1 and X2T2X_2T_2 intersect at a point lying on ω\omega.
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