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

Let AB be the chord of the given circle with centre O. The perpendicular distance from the centre of the circle
to the chord is 8 cm.
Join OB.
Then OM = 8 cm and AB = 30 cm
We know that the perpendicular from the centre of a circle to a chord bisects the chord.
∴ MB=AB^2=30^2 cm=15 cm
From the right Δ OMB, we have:
OB ^2 = OM ^2 + MB ^2
⇒ OB^ 2 = 8^ 2 + 15^ 2
⇒ OB^ 2 = 64 + 225
⇒ OB ^2 = 289
⇒ OB=289 cm=17 cm
Hence, the required length of the radius is 17 cm.