In a right-angled triangle, the leg is 7 and the hypotenuse is 25, find the radius of the circle inscribed in the triangle.

Let’s call the triangle ABC, where AB, BC are the legs, AC is the hypotenuse. We know one leg and the hypotenuse, let this leg be AB, then we find the length of the second leg according to the Pythagorean theorem:

BC ^ 2 = AC ^ 2 – AB ^ 2;

BC ^ 2 = 25 ^ 2 – 7 ^ 2;

BC ^ 2 = 625 – 49;

BC ^ 2 = 576;

BC = 24 cm.

We have all three sides of the triangle, we can find the radius of the circle inscribed in the triangle, as:

r = (a + b – c) / 2, where a, b – legs, c – hypotenuse.

r = (7 + 24 – 25) / 2 = 3 cm.

Answer: the radius of the inscribed circle is 3 cm.