In a right-angled triangle ABC, the legs are known: AC = 5 BC = 12. Find the radius of the circle inscribed in the triangle.

In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 25 + 144 = 169.

AB = 13 cm.

Determine the area of the triangle ABC.

Savs = BC * AC / 2 = 12 * 5/2 = 30 cm2.

Let’s calculate the semiperimeter of the triangle ABC.

p = (AB + BC + AC) = (13 + 12 + 5) / 2 = 30/2 = 15 cm.

Then the radius of the inscribed circle is:

R = OH = Savs / p = 30/15 = 2 cm.

Answer: The radius of the circle is 2 cm.