TUYMAADA 2019 J2

A triangle $ABC$ with $AB < AC$ is inscribed in a circle $\omega$ . Circles $\gamma_1$ and $\gamma_2$ touch the lines $AB$ and $AC$ , and their centres lie on the circumference of $\omega$ . Prove that $C$ lies on a common external tangent to $\gamma_1$ and $\gamma_2$ .