Question

In a circle of radius 13 cm, a chord is at a distance of 12 cm from the center of the circle. Find the length (in cm) of the chord.

• A. 5 cm
• B. 10 cm
• C. 12 cm
• D. 8 cm

Hint:

The perpendicular from the center of a circle to a chord bisects the chord.

Answer 1

The Correct Option is B

Let the chord length be \(2x\). The distance from the circle's center to the chord is 12 cm, and the radius is 13 cm.
By forming a right triangle with the radius, the perpendicular distance from the center to the chord, and half the chord length, the Pythagorean theorem yields:
\[13^2 = 12^2 + x^2 \implies 169 = 144 + x^2 \implies x^2 = 25 \implies x = 5\] Thus, the chord's length is \(2x = 2 \times 5 = 10 \text{ cm}\).