MathNet 2016-part-06 — 184 problems (EN–VI) Question 178

Let $O$ be a circumcenter of a right triangle. The circle with smaller radius and center at point $O$ is tangent to the greater cathetus and the height of the triangle from the right angle.
Find the acute angles of the right triangle and the relation between the radii of the circumcircle and the other circle.
(Bogdan Rublyov)