# In triangle ABC, angle C is 90 degrees, AC is 8, BC is 8√15 find the radius of the circumscribed circle.

September 12, 2021 | education

| In a right-angled triangle ABC, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 8 ^ 2 + (8 * √15) ^ 2 = 64 + 960 = 1024.

AB = 32 cm.

Since the circle is described around a right-angled triangle, the degree measure of the arc AB is equal to two values of the angle ACB, then the arc AB = 2 * 90 = 180, and then the hypotenuse AB is the diameter of the circumscribed circle.

Then R = OB = AB / 2 = 32/2 = 16 cm

Answer: The radius of the circumscribed circle is 16 cm.

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