[ Right triangle with an angle in ]

The hypotenuse $AB$ of the right triangle $ABC$ is 2 and is a chord of a certain circle. The leg $AC$ is 1 and lies inside the circle, and its extension intersects the circle at point $D$, with $CD=3$. Find the radius of the circle.
The leg $A C$ is equal to half the hypotenuse $A B$, so $\angle A=60^{\circ}$. In addition, $A D=2 A B$, so the angle $A B D-$ is a right angle. Therefore, $A D$ is the diameter of the circle.

## Answer

2.