The radii of the intersecting circles are 13 and 16, and the length of their common

The radii of the intersecting circles are 13 and 16, and the length of their common chord is 12. Find the distance between the centers of the circles.

By the property of a common chord of two intersecting circles, it is perpendicular to the line of centers and is divided in half. Then AH = BH = AB / 2 = 12/2 = 6 cm, and triangles AOH and AO1H are rectangular.

Then, by the Pythagorean theorem:

OH ^ 2 = OA ^ 2 – AH ^ 2 = 256 – 36 = 220.

OH = √220 = 2 * √55 cm.

O1H ^ 2 = O1A ^ 2 – AH ^ 2 = 169 – 36 = 133.

О1Н = √133 cm.

Then OO1 = 2 * √55 + √133 cm.

Answer: Between the centers of the circles 2 * √55 + √133 cm.