In a triangle, abc bc = √145, the angle c is 90. The radius of the circumscribed circle is 8.5. Find the AC.

If a right-angled triangle is inscribed in a circle, then the hypotenuse of a right-angled triangle will lie on the diameter of the circle.

Since the radius of the circumscribed circle is 8.5, it means that the diameter of the circle circumscribed about the triangle ABC is 8.5 * 2 = 17. And therefore, the hypotenuse AB of the triangle ABC is 17.

We calculate the length of the side AC of the triangle ABC by the Pythagorean theorem:

AC² = AB² – BC² = 17² – (√145) ² = 289 – 145 = 144.

AC = √144 = 12.

Answer: the length of the speaker is 12.