Question

ABC is an isosceles triangle with ab is equal to AC and the bisector of Angle B and angle C intersect each other at O prove that BO equal to C O and AO is the bisector of the angle BAC

Answer 1

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Answer 2

Answer:

Given :

• AB = AC

• The bisector of B and C intersects each other at O

To Prove :

I) OB = OC

II) AO bisects A

Proof :

I) ABC is an isosceles triangle in which AB = AC

C = B ( Angle opposite to the equal sides)

=> OCA + OCB = OBA + OBC

OB bisects B and OCA bisects C

=> OBA = OBC and OCA = OCB

=> OCB + OCB = OBC + OBC

=> 2OCB = 2OBC

=> OCB = OBC

Hence, OB = OC (Sides opposite to equal angles)

II) In ΔAOB and Δ AOC

AB = AC (Given)

OA = OA (Common)

OB = OC (Proved above)

Hence, ΔAOB ≈ ΔAOC ( by SSS)

OAB = OAC (CPCTC)

$\boxed{\pink{Proved}}$