In triangle ABC, angle C is 90 °, BC = √135. The radius of the circle around this triangle is 8. Find AC.
| September 15, 2021 | education
One of the properties of a right triangle is that the midpoint of the hypotenuse is the center of the circumscribed circle. In our case, knowing the radius of the circumscribed circle, we get:
AB = 2 * R = 2 * 8 = 16.
Find the unknown AC leg:
AC = √ (AB² – BC²) = √ (256 – 135) = √121 = 11.
Answer: the AC leg is 11.
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