Question 25
On the altitude to the side $AC$ of an isosceles triangle $ABC$ with apex $B$, a point $D$ is chosen so that the line $AC$ is tangent to the circumcircle $\mathcal{K}$ of triangle $ABD$. Let $E$ be a point on the circle $\mathcal{K}$ such that the chord $DE$ is perpendicular to the chord $AB$. Prove that the triangles $ABE$ and $ABC$ are congruent.