In triangle ABC, it is known that AC = 8, BC = 15, angle C is 90 (degrees). Find the radius of the circle
| August 3, 2021 | education
In triangle ABC, it is known that AC = 8, BC = 15, angle C is 90 (degrees). Find the radius of the circle circumscribed about this triangle.
The center of a circle circumscribed around a right-angled triangle coincides with the center of the hypotenuse. This means that the radius of this circle is half the hypotenuse.
Let’s use the Pythagorean theorem: the square of the hypotenuse is equal to the sum of the squares of the legs:
AB ^ 2 = 8 * 8 + 15 * 15;
AB ^ 2 = 64 + 225;
AB ^ 2 = 289;
AB = 18.
The radius of the circumscribed circle = 18/2 = 9.
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