Question

the length of two parallel chords of a circle 8 cm and 6 CM . if the smaller chords is at a distance of 4 cm from the centre, what is the distance of the Other chord from the centre

Answer 1

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Let AB and CD are two parallel chords of a circle having length 6 cm and 8 cm and radius is O.

Let radius of the circle is r cm.

Now draw OP perpendicular to AB and OQ perpendicular to CD.

since OP is perpendicular to AB and OQ is perpendicular to CD and AB || Cd

So points O, P and Q are collinear.

From figure, OP = 4.

P, Q are the mid points of AB and CD.

So AP = PB = AB/2 = 6/2 = 3

CQ = QD = CD/2 = 8/2 = 4

Now in ΔOAP

      OA2 = OP2 + AP2

=> r2 = 42 + 32

=> r2 = 16 + 9

=> r2 = 25

=> r = √25

=> r = 5

Again from ΔOCQ

     OC2 = OQ2 + CQ2

=> r2 = OQ2 + 42

=> 52 = OQ2 + 16

=> OQ2 = 25 - 16

=> OQ2 = 9

=> OQ = √9

=> OQ = 3



So the distance of chord from the centre is 3 cm