Question 167
Find all right-angled triangles with integral lengths of sides in which one can inscribe two congruent circles which satisfy the following conditions:
* Their radius is a prime number.
* The circles touch externally.
* Both of the circles are tangent to the hypotenuse and each of them is tangent to a different leg of a triangle.
* Their radius is a prime number.
* The circles touch externally.
* Both of the circles are tangent to the hypotenuse and each of them is tangent to a different leg of a triangle.