A rectangular triangle with 12 cm and 16 cm legs is inscribed in a circle. find its radius

We are given a right-angled triangle with the lengths of its legs 12 cm and 16 cm. And we need to find the radius of the circumscribed circle. It is known that the radius of the circumscribed circle is half the length of the hypotenuse of a triangle.

Let’s apply the Pythagorean theorem to calculate the length of the hypotenuse:

c ^ 2 = a ^ 2 + b ^ 2.

The square of the hypotenuse is equal to the sum of the squares of the legs. We substitute the values into the formula and perform the calculations:

c = √ (a ^ 2 + b ^ 2) = √ (16 ^ 2 + 12 ^ 2) = √ (256 + 144) = √400 = 20 cm.

Divide the length of the hypotenuse by 2 and get:

c / 2 = 20/2 = 10 cm radius of the circumscribed circle.