CZ-SK-MO 2021 Problem 6

An acute triangle $ABC$ is given. Let us denote $X$ for each of its inner points $X_a, X_b, X_c$ its images in axial symmetries sequentially along the lines $BC, CA, AB$ . Prove that all $X_aX_bX_c$ triangles have a common interior point.

(Josef Tkadlec)