Q. 24.2( 31 Votes )

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

Answer :

Given radius of circle is 13cm

OA = OD = 13cm

OQ = OP = 16cm

We know that a perpendicular drawn from the centre of a circle on its chord bisects

the chord.

CQ = QD

CD = 2×QD

In right angled ΔOQD using the Pythagoras theorem

OD^{2} = OQ^{2} + QD^{2}

13^{2} = 5^{2} + QD^{2}

169 = 25 + QD^{2}

QD^{2} = 144

QD = 12cm

Therefore the length of chord CD = 2×12 = 24cm

We know that The chords of a circle equidistant from the center of a circle are congruent

As AB and CD are equidistant, they are equal in length.

∴ AB = CD = 24cm

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