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# In a circle of radius 5 cm, AB and AC are two chords such that AB = AC = 6 cm. Find length of chord BC.

Asked by Topperlearning User 4th June 2014, 1:23 PM

Given - AB and AC are two equal words of a circle, therefore the centre of the circle lies on the bisector of BAC.

OA is the bisector of BAC.

Again, the internal bisector of an angle divides the opposite sides in the ratio of the sides containing the angle.

P divides BC in the ratio = 6 : 6 = 1 : 1.

P is mid-point of BC.

OP BC.

In ABP, by Pythagoras theorem,

In right OBP, we have

Equating (1) and (2), we get

Putting AP in (1), we get

or,alternate method:

Area of AOB by Heron's formula

arAOB) =

Also arAOB =

BM = h = 4.8 cm

BC = 2 BM = 9.6 cm.

Answered by Expert 4th June 2014, 3:23 PM
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