Question 28
Let $D$ be an interior point of the side $BC$ of a right triangle $ABC$ with the right angle at $C$. Denote by $\mathcal{K}$ the circumcircle of triangle $ABD$. Let $E$ be a point on $\mathcal{K}$ such that the chord $DE$ is perpendicular to $AB$. Prove that the triangle $AEB$ is isosceles with apex $B$ if and only if $CA$ is tangent to the circle $\mathcal{K}$.