Question

O is centre of the circle. Find the length of radius, if the chord of length 24 cm is at a distance of 9 cm from the centre of the circle.

Answer 1

Join OA.

Let the perpendicular drawn from point O to the chord AB be P.

We know that the perpendicular drawn from the centre of the circle to the chord bisects the chord.

So, AP = `"AB"/2 = 24/2` = 12 cm

In Δ OPA,

We apply the Pythagoras theorem,

OP² + AP² = OA²

⇒ 9² + 12² = OA²

⇒ OA² = 81 + 144 = 225

⇒ OA = `sqrt225` 15 cm 

Hence, the radius of the circle is 15 cm.