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Two circles and tangents

Source: Baltic Way 2023/15

November 11, 2023
geometry

Problem Statement

Let ω1\omega_1 and ω2\omega_2 be two circles with no common points, such that any of them is not inside the other one. Let M,NM, N lie on ω1,ω2\omega_1, \omega_2, such that the tangents at MM to ω1\omega_1 and NN to ω2\omega_2 meet at PP, such that PM=PNPM=PN. The circles ω1\omega_1, ω2\omega_2 meet MNMN at A,BA, B. The lines PA,PBPA, PB meet ω1,ω2\omega_1, \omega_2 at C,DC, D. Show that ∠BCN=∠ADM\angle BCN=\angle ADM.
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