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


OD2 = OQ2 + QD2


132 = 52 + QD2


169 = 25 + QD2


QD2 = 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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