A semicircle is inscribed in a right-angled triangle with legs 5 cm and 12 cm and a hypotenuse

A semicircle is inscribed in a right-angled triangle with legs 5 cm and 12 cm and a hypotenuse of 13 cm. Find the radius of the semicircle.

Let us find the radius of the inscribed circle ro by the classical formula:

r = √ (p – a) * (p – b) * (p – c) / p, where a, b, c are sides, p = 1/2 (a + b + c).

P = 1/2 * (5 + 12 + 13) = 10.

r = √5 * (-2) * (-3) / 10 = √25 / 10 = 5 / √10.

Then the required radius is equal to:

2 * 5 / √10 = √10 cm.