The radius of a circle circumscribed about a right-angled triangle is 12.5, and one of its legs is 20.

univerkov | September 28, 2021 | education

The radius of a circle circumscribed about a right-angled triangle is 12.5, and one of its legs is 20. Find the other boat of this triangle.

Since triangle ABC is rectangular and inscribed in a circle, the inscribed angle ABC = 90, and the degree measure of the arc on which it rests is 2 * 90 = 180.

Then the hypotenuse AC is the diameter of the inscribed triangle.

AC = 2 * R = 2 * 12.5 = 25 cm.

By the Pythagorean theorem, we determine the length of the BC leg.

BC ^ 2 = AC ^ 2 – AB ^ 2 = 625 – 400 = 225.

BC = 15 cm.

Answer: The length of the other leg is 15 cm.

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