Question 97
Let $K_1$ be a circle with the center $S_1$ and the radius $r$. Let $K_2$ be a circle with the center $S_2$, lying on the circle $K_1$, and the radius $\frac{2}{3}r$. Let $A$ be the point of intersection of the line $S_1S_2$ and the circle $K_2$ that lies in the exterior of the circle $K_1$. Let $C$ denote one of the intersection points of the circles $K_1$ and $K_2$. The line $AC$ also intersects the circle $K_1$ at the point $D$. Let $H$ be the orthogonal projection of the point $D$ onto the line $S_1S_2$. Prove that the point $H$ lies on the circle $K_2$.