Question

A chord of length 30 cm is drawn at a distance of 8 cm from the centre of a circle. Find out the radius of the circle.

Answer 1

Consider AB as the chord of the circle with O as the centre

Construct OL ⊥ AB

From the figure, we know that OL is the distance from the centre of the chord

It is given that AB = 30 cm and OL = 8 cm

Perpendicular from the centre of a circle to a chord bisects the chord

So, AL = 15 cm

Consider $\Delta$ OLA

Using the Pythagoras theorem, $O{A}^2=O{L}^2+A{L}^2$

$O{A}^2=8^2+{15}^2$

$O{A}^2=64+225$

$O{A}^2=289$

$OA=\sqrt{289}$

$OA=17$ cm

Therefore, the radius of the circle is 17 cm