# In triangular ABC it is known that AC = 8 BC = 15 angle C is equal to 90 degrees.

In triangular ABC it is known that AC = 8 BC = 15 angle C is equal to 90 degrees. Find the radius of the circumscribed circle around this triangle.

Since the angle of triangle C is 90 °, then triangle ABC is a right-angled triangle, AC and BC are the legs of this right-angled triangle.

When a right-angled triangle is inscribed in a circle, the hypotenuse of the triangle lies on the diameter of this circumscribed circle. Therefore, if we find the length of the hypotenuse of the triangle ABC, we will find the length of the diameter of the circle.

Let us find the length of the hypotenuse AB by the Pythagorean theorem:

AB² = AC² + BC² = 8² + 15² = 64 + 225 = 289.

AB = √289 = 17.

Since the diameter of the circle is 17, and the radius is half the diameter, we calculate the length of the radius of the circle described around this triangle: 17: 2 = 8.5.

Answer: the radius of the circumscribed circle is 8.5.

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