Given a right-angled triangle ABC, a straight line angle C. Find the radius of the circle circumscribed
| June 2, 2021 | education
Given a right-angled triangle ABC, a straight line angle C. Find the radius of the circle circumscribed by this triangle if AC = 3, BC = 4.
1. Let us denote by the symbol R the radius of the circumscribed circle.
2. The center of a circle circumscribed about a right-angled triangle is a point located in the middle of the hypotenuse. Therefore, to find the radius of the circle, we calculate the length of the hypotenuse AB, using the formula of the Pythagorean theorem:
AB = √AC² + BC² = √3² + 4² = √9² +16 = √25 = 5 centimeters.
2. R = AB: 2 = 2.5 centimeters.
Answer: R = 2.5 centimeters.
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