The center of the circle circumscribed about the triangle ABC lies on the side AB.

The center of the circle circumscribed about the triangle ABC lies on the side AB. The radius of the circle is 13. Find AC if BC = 24.

Since, by condition, the center of the circle lies on the side AB of the triangle, AB is the diameter of the circumscribed circle, therefore, AB = 2 * R = 2 * 13 = 26 cm.

The angle ACB is 90, since it is based on the diameter of the circle, then the triangle ABC is rectangular.

Let us determine, according to the Pythagorean theorem, the length of the leg AC.

AC ^ 2 – AB ^ 2 – BC ^ 2 = 26 ^ 2 – 24 ^ 2 = 676 – 576 = 100.

AC = 10 cm.

Answer: Speaker length = 10 cm.