Question 2
In a triangle $ABC$, denote $D$ the orthogonal projection of the point $C$ onto the line $AB$, denote $E$ the orthogonal projection of the point $D$ onto the line $AC$, and denote $P$ the midpoint of the line segment $CD$. Let $K_1$ be the circumscribed circle of the triangle $ABC$, and let $K_2$ be the circle of radius $CD$ and center $C$. Prove that the line $EP$ passes through the intersection points of the circles $K_1$ and $K_2$ if and only if the angle $\angle ACB$ is a right angle.