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Question

Bisectors of the angles B and C of an isosceles triangle with AB = AC intersect each other at O. BO is produced to a point M. Then which of the following options is correct?

A
MOC=BAC
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B
MOC=ABC
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C
MOC=MBC
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D
MOC=OCB
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Solution

The correct option is B MOC=ABC

Bisectors of the angles B and C of an isosceles triangle ΔABC with AB = AC intersect each other at O. BO is produced to a point M.


In ΔABC, we have
AB=AC (given)
ABC=ACB [ Angles opposite to equal sides of a triangle are equal.]
12ABC=12ACB
i.e., 1=2
MOC=1+2 [ Exterior angle of a triangle is equal to the sum of interior opposite angles]
MOC=21 [1=2]
Hence, MOC=ABC.
[ 1=12ABC ]


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