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