Question

A chord of length 16 cm is drawn in a circle of radius 10 cm. Find the distance of the chord from the centre of the circle.

Answer 1

Let AB be the chord of the given circle with centre O and a radius of 10 cm.
Then AB =16 cm and OB = 10 cm
From O, draw OM perpendicular to AB.
We know that the perpendicular from the centre of a circle to a chord bisects the chord.
∴ BM = 8 cm
In the right Δ OMB, we have:
OB ^2 = OM ^2 + MB^ 2 (Pythagoras theorem)
⇒ 10 ^2 = OM ^2 + 8^ 2
⇒ 100 = OM ^2 + 64
⇒ OM^ 2 = (100 - 64) = 36
⇒ OM=36 cm=6 cm
Hence, the distance of the chord from the centre is 6 cm.