The sides of a right-angled triangle are 12 cm, 16 cm, 20 cm. Find the radius of the circle inscribed in this triangle.

Solution:

The radius is:

r = √ (p – a) * (p – b) * (p – c) / p.

Next, we find the perimeter of the triangle:

p = (12 + 16 + 20) / 2 = 48/2 = 24.

We substitute all available values in the formula:

r = √ (24 – 12) * (24 – 16) * (24 – 20) / 24 = √ (12 * 8 * 4) / 24 = √384 / 24 = √16 = 4 cm.

Answer: the radius of the circle inscribed in the triangle is 4 cm.