What is the length (in cm) of the chord of a circle whose radius is 13 cm and whose perpendicular distance from the chord to the centre is 5 cm?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 24.
OA (radius) = 13 cm and OM = 5 cm
Triangle OMA is a right triangle, with ∠OMA = 90°
So,
OA2 = OM2 + AM2
⇒ 132 = 52 + AM2
⇒ 169 = 25 + AM2
⇒ AM2 = 169 - 25 = 144
⇒ AM = √144 = 12
The perpendicular from the center of a circle to a chord bisects the chord.
So, AM = MB
Now, AB = 2AM = 2 × 12 = 24 cm
The length of the chord is 24 cm.