Question

A chord of length 10 cm, is at a distance of 12 cm from the centre of the circle. Find the radius of the circle.

Answer 1

Given: A chord AB = 10 cm and its distance from the centre O is OM = 12 cm.

Step-wise calculation: 

The perpendicular from the centre bisects the chord.

So, `AM = (AB)/2`

= 5  cm

In right triangle OAM,

By Pythagoras:

OA² = OM² + AM² 

r² = 12² + 5²

= 144 + 25

= 169

`r = sqrt(169)` 

r = 13 cm

Radius of the circle = 13 cm.