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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

None of these

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Solution

The correct option is B

MOC=ABC


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


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


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