Find the radius of the circle inscribed in a right-angled triangle with legs 20 and 48.

1. In geometry, a formula is known for finding the value of the radius r of a circle inscribed in a right-angled triangle: r = (a + b – c): 2, where a and b are legs, and c is the hypotenuse of a triangle.

2. In the problem statement it is given that a = 20, b = 48.

Determine what is the length of the hypotenuse.

For this we use the Pythagorean theorem:

c² = a² + b², that is, c = √ 20² + 48² = √2704 = 52.

3. Find r circles:

r = (20 + 48 – 52): 2 = 16: 2 = 8.

Answer: The radius of the given inscribed circle is 8.