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?
∠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.]
⇒12∠ABC=12∠ACB , i.e., ∠1=∠2
[∵ Exterior angle of a triangle is equal to the sum of interior opposite angles]
⇒ Ext. ∠MOC=∠1+∠2 = 2∠1 [∵∠1=∠2]
Hence, ∠MOC=∠ABC. [∵ ∠1=12∠ABC]