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prove that point lies on a common external tangent of 2 circles

Source: Tuymaada Olympiad 2019 junior p2

July 22, 2019
geometrycircumcirclecommon tangentscircles

Problem Statement

A triangle ABCABC with AB<ACAB < AC is inscribed in a circle ω\omega. Circles γ1\gamma_1 and γ2\gamma_2 touch the lines ABAB and ACAC, and their centres lie on the circumference of ω\omega. Prove that CC lies on a common external tangent to γ1\gamma_1 and γ2\gamma_2.
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