Question

The radius of a circle is 17 cm and the length of perpendicular from centre to a chord is 8 cm. Find the length of the chord.

Answer 1

Given: Radius OA = 17 cm, perpendicular from centre to chord OP = 8 cm.

Step-wise calculation:

1. The perpendicular from the centre to a chord bisects the chord.

So, half the chord = AM (say) where `AM = sqrt(OA^2 - OP^2)`.

2. Compute half-chord:

`AM = sqrt(17^2 - 8^2)`

= `sqrt(289 - 64)`

= `sqrt(225)`

= 15 cm

3. Full chord length

= 2 × AM

= 2 × 15

= 30 cm

The length of the chord is 30 cm.