Question

Radius of a circle is 34 cm and the distance of the chord from the centre is 30 cm, find the length of the chord.

Answer 1

Let O be the center of the circle and seg AB is its chord.

seg OC ⊥ chord AB such that, A-C-B

OA = 34 cm

OC = 30 cm

In ∆OCA, From Pythagoras theorem,

OA² = OC² + AC²

∴ 34² = 30² + AC²

∴ 1156 = 900 + AC²

∴ AC² = 1156 – 900

∴ AC² = 256

∴ AC = `sqrt(256)`

∴ AC = 16 cm

∴ AC = `1/2` AB      ...(The perpendicular drawn from the center of the circle to the chord bisects the chord.)

∴ 16 = `1/2` AB

∴ AB = `16 xx 2`

∴ AB = 32 cm