Two circles intersect and have a common chord 24 cm long. The centers of the circles are 21 cm apart. The radius of one circle is 13 cm. Find the radius of the other circle

Answer 1

Hello Paul,

Looks like the radii are 13 and 20. Can't draw it but can create two opposing rt triangles. The hypotenuse of each is the radius of the respective circle, the vertical side is 1/2 of the length of the chord 24/2 = 12. So for the circle with radius 13 it's a 5 - 12 - 13 rt. triangle. If the center-to-center dimension is 21, then the base of the other, opposing, rt triangle is 21 - 5, or 16. So for the larger circle, you can solve for its hypotenuse, which is its radius. 12² + 16² = x² and x = 20. OK?

Answer 2