In triangle ABC, angle C is straight, BC = 15. The radius of a circle circumscribed about a triangle is 8.5. Find the AC.
| September 20, 2021 | education
A right-angled triangle ABC is inscribed in a circle.
Then the hypotenuse AB is the diameter of this circle.
AB = 8.5 * 2 = 17.
AC and BC are the legs of a right-angled triangle ABC.
Find AC by the Pythagorean theorem.
AC = √ (AB² – BC²).
AC = √ (17² – 15²) = √ (17 – 15) (17 + 15) = √ (2 * 32) = √64 = 8.
Answer: AC = 8.
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