#### Answer

The radii of the circles are about 8.5 cm long.

#### Work Step by Step

The given information tells you that the triangles formed by half of the chord, their perpendicular bisectors, and the radii of the circles, are 45 45 90 triangles. Therefore, the radii of the triangles is equal to half the length of the chord multiplied by the square root of two:
r=.5(12)($\sqrt 2$)
r=6$\sqrt 2$$\approx$8.5