Problem #PRU-5190

Problem

Recall that a line is tangent to a circle if they have only one point of intersection, a circle is called inscribed in a polygon if it is tangent to every side as a segment of that polygon.
In the triangle $CDE$ the angle $\mathrm{\angle }CDE={90}^{\circ }$ and the line $DH$ is the median. A circle with center $A$ is inscribed in the triangle $CDH$ and is tangent to the segment $DH$ in its middle, let’s denote it as $G$, so $GH=DG$. Find the angles of the triangle $CDE$.