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 the circle to a chord bisects the chord, use Pythagoras theorem to find chord length.

Answer 1

The Correct Option is B

Let the circle have center O, radius r = 13 cm, and chord AB at a distance d = 12 cm from the center.
Draw a perpendicular from O to chord AB, meeting at point M. Then, OM = 12 cm and AM = MB = AB/2.
Using the right triangle OAM, by Pythagoras theorem:
\[OA^2 = OM^2 + AM^2\]
\[13^2 = 12^2 + AM^2\]
\[169 = 144 + AM^2\]
\[AM^2 = 169 - 144 = 25\]
\[AM = 5 cm\]
Length of chord AB = 2 × AM = 2 × 5 = 10 cm.