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 $OL\perp AB$. Join OA.

Here, $OL=5cm,OA=13cm$.

In right triangle OLA,

$O{A}^2=O{L}^2+A{L}^2$

${13}^2=5^2+A{L}^2$

$A{L}^2=144$

$AL=12$

Since the perpendicular from the centre to a chord bisects the chord. Therefore,

$AB=2AL=2\times 12=24cm$