# In a right-angled triangle, the legs are 9 and 12 cm. Find the radius of the circumscribed circle.

July 29, 2021 | education

| Since the radius is the distance from the center of the circle to any point on it, and the center of the circle circumscribed around a right-angled triangle coincides with the point that divides the hypotenuse in half, we find the hypotenuse and divide it in two.

We find the hypotenuse by the Pythagorean theorem. The hypotenuse squared is equal to the sum of the squares of the legs. Then:

c ^ 2 = 9 ^ 2 + 12 ^ 2.

c ^ 2 = 225.

s = 15 (cm).

Then the radius is:

15: 2 = 7.5 (cm).

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