SHARYGIN 2020 Problem 3

Let $ABC$ be a triangle with $\angle C=90^\circ$ , and $D$ be a point outside $ABC$ , such that $\angle ADC=\angle BAC$ . The segments $CD$ and $AB$ meet at point $E$ . It is known that the distance from $E$ to $AC$ is equal to the circumradius of triangle $ADE$ . Find the angles of triangle $ABC$ .