Find the chord length of a circle with a radius of 13 cm. If the distance from the center of the circle to the chord is 5 cm.

univerkov | May 14, 2021 | education

Consider a right-angled triangle AOC, in which the hypotenuse AO is the radius of the circle, the leg OS is equal to the distance from the center of the circle to the chord, and the leg AC is equal to half the length of chord AB.

By the Pythagorean theorem: AO ^ 2 = OC ^ 2 + AC ^ 2.

13 ^ 2 = 5 ^ 2 + AC ^ 2.

AC ^ 2 = 169 – 25 = 144.

AC = 12 cm.

Then AB = 2 * AC = 2 * 12 = 24 cm.

Answer: The length of the chord AB = 24 cm.

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