Question

Two non-congruent circles intersect and have a common chord 40 cm

long. The centers of the circles are 63 cm apart. The radius of one circle is
52 cm. Find the radius of the other circle.
Please include all work and sketch

Answer 1

• 25 cm

Explanation:

The chord and the segment between the centers form the diagonals of a kite with each pair of side being the radius of the circles.

As we know the long diagonal bisects the shorter one and they are perpendicular.

Using Pythagorean, lets find the distance between the center of a greater circle and the chord:

• 52² - (40/2)² = 2304 ⇒ √2304 = 48 cm

The distance from the center of smaller circle and the chord is:

• 63 - 48 = 15 cm

Now using Pythagorean again, find the radius of the smaller circle:

• 15² + (40/2)² = 625 ⇒ √625 = 25 cm