CBSE Class 9 Answered
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 | 04 Jun, 2014, 01:23: PM
Expert Answer
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 | 04 Jun, 2014, 03:23: PM
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