In the triangle ABC, the length of side AB is 6, the length of side BC is 8, and the length of side AC is 10. What is the radius of the circumscribed circle?
Correct: C
To find the radius of the circumscribed circle, we need to use the formula R = abc / (4A), where a, b, and c are the side lengths of the triangle, and A is its area. The area of the triangle can be found using Heron's formula, which is A = √(s(s - a)(s - b)(s - c)), where s is the semi-perimeter of the triangle. The semi-perimeter is given by s = (a + b + c)/2 = (6 + 8 + 10)/2 = 12. Plugging this value into Heron's formula, we get A = √(12(12 - 6)(12 - 8)(12 - 10)) = √(12 * 6 * 4 * 2) = √(576) = 24. Then, the radius of the circumscribed circle is R = abc / (4A) = (6 * 8 * 10) / (4 * 24) = 480 / 96 = 5.