In a circle whose radius is 20 cm, a chord is drawn at a distance of 12 cm from the center of the circle

In a circle whose radius is 20 cm, a chord is drawn at a distance of 12 cm from the center of the circle. What is the length of this chord?

Construct the radii of the circle to the ends of the chord AB.

Then the triangle AOB is isosceles, since OA = OB = R = 20 cm.

The distance from the center of the circle to the chord is the height OH of the isosceles triangle AOB. The height OH is also the median of the triangle AOB, then AH = BH = AB / 2, and the triangle AOH is rectangular.

In the right-angled triangle AOН, by the Pythagorean theorem, we determine the length of the leg AН.

AH ^ 2 = AO ^ 2 – OH ^ 2 = 400 – 144 = 256.

AH = 16 cm.

Then AB = AH * 2 = 16 * 2 = 32 cm.

Answer: The length of the chord AB is 32 cm.