The radii of two circles having a common center are in the ratio 2: 3.

The radii of two circles having a common center are in the ratio 2: 3. The chord of the larger circle touches the smaller circle and is equal to 20 cm.Find the radii of the circles

We denote by r and R the radii of the smaller and larger circles, then, by the problem statement, we obtain the equation:

r / R = 2/3;

3r = 2R;

R = 3/2 r.

Since the chord touches the smaller circle, then at the point of tangency it makes an angle of 90 degrees with a small radius and is divided in half, then by the Pythagorean theorem:

r ^ 2 + 10 ^ 2 = R ^ 2.

9/4 r ^ 2 – r ^ 2 = 100;

r ^ 2 = 80;

r = √80.

Then:

R = 3/2 * √80.