In triangle ABC BC = 4, angle C is 90 degrees. The radius of the circumscribed circle of this triangle is 2.5. Find AC.
| January 17, 2021 | education
∆АВС – straight. A circle is described around it. According to the theorem, in a right-angled triangle, the center of the circumscribed circle lies in the middle of the hypotenuse.
Thus, AB is the diameter of the circle and its length is 2 * r.
From the conditions r = 2.5, which means AB = 2 * 2.5 = 5.
Because .∆ABS is a straight line, then by the Pythagorean theorem AB ^ 2 = BC ^ 2 + AC ^ 2.
Substitute the known values and find AC = √ (AB ^ 2 – BC ^ 2) = √ (25 – 16) = √9 = 3.
Answer: AC side = 3.
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