# Line segments AB and CD are chords of a circle. Find the distance from the center of the circle to the chord CD if AB = 20

**Line segments AB and CD are chords of a circle. Find the distance from the center of the circle to the chord CD if AB = 20, CD = 48, and the distance from the center of the circle to the chord AB is 24.**

Let’s denote by point O – the center of the circle.

Next, consider the triangle AOB.

This triangle is isosceles (since its sides are equal to the radius of the circle). The distance from the center of the circle O to the chord AB is the height of this triangle, and, therefore, the median.

Let’s mark the point Y – the intersection of the height and AB.

Find the hypotenuse of a right-angled triangle OPA, which is also the radius of the circle: r = √ (10² + 24²) = √676 = 26 cm.

Next, we find the leg, which is the height of the isosceles triangle CD, and thus is the required distance to the chord CD:

h = √ (26² – 24²) = √100 = 10 cm.

Answer: The distance to the CD chord is 10 centimeters.