Question

Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm.

Answer 1

Let AB be a chord of a circle with centre O and radius 13 cm. Draw OL ⊥ AB.
Join OA. Clearly, OL = 5 cm and OA = 13 cm.
In the right triangle OLA, we have 
OA² = OL² + AL²

⇒ 13² = 5² + AL²
⇒  AL² = 144 cm²
⇒  AL = 12 cm
Since, the perpendicular from centre to the chord bisects the chord. Therefore,
AB = 2AL = 2 x 12 cm = 24 cm.