Fixed two circles $w_1$ and $w_2$, $\ell$ one of their external tangent and $m$ one of their internal tangent . On the line $m$, a point $X$ is chosen, and on the line $\ell$, points $Y$ and $Z$ are constructed so that $XY$ and $XZ$ touch $w_1$ and $w_2$, respectively, and the triangle $XYZ$ contains circles $w_1$ and $w_2$. Prove that the centers of the circles inscribed in triangles $XYZ$ lie on one line. (P. Kozhevnikov)