Question 160
Let $\triangle ABC$ be an isosceles triangle with the apex at $B$ and choose a point $D$ on the altitude from $B$ such that $AC$ is tangent to the circumcircle $\mathcal{K}$ of the triangle $ABD$. Let $E$ be a point on $\mathcal{K}$ such that the chord $DE$ is perpendicular to the chord $AB$. Prove that triangles $ABE$ and $ABC$ are congruent.