Question

Radius of circle is 10 cm. There are two chords of length 16 cm each. What will be the distance of these chords from the centre of the circle?

Answer 1

Let, O be the center of the circle and seg AB and seg CD are its congruent chords.

seg OM ⊥ seg AB such that, A-M-B and seg ON ⊥ seg CD such that, C-N-D.

OB = OD = 10 cm      ...(Radius of the circle is 10 cm.)

AB = CD = 16 cm      …(Given)

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

∴ MB = `1/2 xx 16`

∴ MB = 8 cm

In ∆OMB, by Pythagoras theorem,

OB² = OM² + MB²

∴ 10² = OM² + 8²

∴ OM² = 100 – 64

∴ OM² = 36

Taking the square root on both sides,

∴ OM = `sqrt(36)`

∴ OM = 6 cm

∴ ON = OM       ...(Congruent chords of a circle are the same distance from the centre.)

∴ ON = 6 cm