Question

16. A chord is at a distance of 5 cm from the centre of a circle of radius 13 cm. The length
of the chord is
a. 25 cm
b. 12 cm
C. 24 cm
d. 9 cm​

Answer 1

The length of the chord is 24 cm.

Let AB be a chord of a circle with centre O and radius 13 cm. Draw OL⊥AB.

Join OA.

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

In right triangle OLA,

${OA}^{2} = {OL}^{2}+{AL}^{2}\\\\{13}^{2}={5}^{2}+{AL}^{2}\\\\{AL}^{2}=169-25\\\\{AL}^{2}=144\\\\AL=\sqrt{144}\\\\\underline{AL=12cm}$

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

AB = 2AL = 2×12 = 24 cm

Answer 2

Answer:

(C) 24cm.....................................