[ Diameter, main properties ]

A circle touches one side of a right angle with vertex $O$ and intersects the other side at points $A$ and $B$. Find the radius of the circle if $O A=a$ and $O B=b$.

#
Drop a perpendicular from the center of the circle to $A B$.

## Solution

Let $O_{1}$ be the center of the circle, $C$ be the point of tangency of the circle with the first side of the angle. Assume that $ab$.

## Answer

$\frac{a+b}{2}$.