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 length of the chord be \(2x\). The distance from the center to the chord is given as 12 cm, and the radius of the circle is 13 cm.
Using the right triangle formed by the radius, the distance from the center to the chord (perpendicular), and half the chord length, we apply Pythagoras theorem:
\[ 13^2 = 12^2 + x^2 \implies 169 = 144 + x^2 \implies x^2 = 25 \implies x = 5 \] Therefore, the length of the chord \(= 2x = 2 \times 5 = 10 \text{ cm}\).