Question 109
Consider a triangle $ABC$ and a line that does not coincide with the triangle sides and passes through the point $A$. This line meets altitudes $BH_2$ and $CH_3$ at the points $D_1$ and $E_1$, respectively. By $D_2$ and $E_2$ we denote points that are symmetrical to $D_1$ and $E_1$ with respect to the sides $AB$ and $AC$, respectively. Prove that the circumcircle of the triangle $D_2AB$ is tangent to the circumcircle of the triangle $E_2AC$.
(Myhailo Plotnikov)
(Myhailo Plotnikov)