MathNet 2017-part-06 — 176 problems (EN–VI) Question 112

Let $ABC$ be a triangle with $AB \neq AC$ and circumcircle $k$. Let the tangent to $k$ through $A$ meet $BC$ at $P$. Let the bisector of $\angle APB$ meet $AB$ at $D$ and $AC$ at $E$. Show that triangle $ADE$ is isosceles.