A circle constructed on the leg of a right triangle as its diameter bisects the hypotenuse. Find the angles of the triangle.

#
If the median of a triangle is its altitude, then the triangle is isosceles.

## Solution

Let the circle constructed with the leg $AC$ of the right triangle $ABC$ as its diameter intersect the hypotenuse $AB$ at its midpoint $M$. Then

$\angle AMC=90^{\circ}$. Therefore, $CM$ is the altitude and median of triangle $ABC$. Hence, triangle $ABC$ is isosceles. Consequently, $AC=BC, \angle A=\angle B=45^{\circ}$.

## Answer

$45^{\circ}, 45^{\circ}, 90^{\circ}$.