Question

In a circle with radius 13 cm, two equal chords are at a distance of 5 cm from the centre. Find the lengths of the chords.

Answer 1

Let, O be the center of the circle and seg AB and seg CD are equal-length chords of the circle.

seg OE ⊥ seg AB such that, A-E-B and seg OF ⊥ seg CD such that, C-F-D.

OA = OD = 13 cm      ...(Radius of the circle is 13 cm.)

In ∆AEO, by Pythagoras theorem,

OA² = OE² + EA²

∴ 13² = 5² + EA²

∴ EA² = 169 – 25

∴ EA² = 144

∴ EA = `sqrt(144)`

∴ EA = 12 cm

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

∴ 12 = `1/2` BA

∴ BA = `12 xx 2`

∴ BA = 24 cm

chord AB ≅ chord CD 

∴ CD = 24 cm