Find the length of the chord AB located at a distance of 9 from the center of the circle O, if the radius of the circle is OA = 15.

univerkov | February 19, 2021 | education

Consider a right-angled triangle AOC, in which the hypotenuse AO is the radius of the circle, the leg OC 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.

15 ^ 2 = 9 ^ 2 + AC ^ 2.

AC ^ 2 = 225 – 81 = 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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