Question

In the circle of radius 5cm.AB and AC are two chords su ch that AB=AC=6cm Find the length of chord BC

Answer 1

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.

Answer 2

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