KöMaL 2019 B5063

In a triangle $ABC$, $BC<AC$ and $\angle ACB$ is a right angle. The tangents drawn from point $A$ to the circle of diameter $BC$ touch it at $C$ and $D$. The line of tangent $AD$ intersects line $BC$ at point $E$. The midpoint of line segment $BC$ is $O$. Prove that the area of triangle $DEO$ equals the area of triangle $AEB$.