Sharygin 2021, correspondence round, problem 6
Sharygin 2021, correspondence round, problem 6 is a plane geometry problem from the Sharygin Geometry Olympiad 2021, correspondence round, problem 6 (grades 8–9): three circles inscribed in an angle.
Problem
Three circles $\Gamma_1$, $\Gamma_2$, $\Gamma_3$ are inscribed into an angle (the radius of $\Gamma_1$ is the minimal, and the radius of $\Gamma_3$ is the maximal) in such a way that $\Gamma_2$ touches $\Gamma_1$ and $\Gamma_3$ at points $A$ and $B$ respectively. Let $\ell$ be a tangent at $A$ to $\Gamma_1$. Consider circles $\omega$ touching $\Gamma_1$ and $\ell$. Find the locus of meeting points of common internal tangents to $\omega$ and $\Gamma_3$.
Source Sharygin Geometry Olympiad 2021, correspondence round, problem 6 (grades 8–9)
The diagram
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