In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that : (i) OB = OC (ii) AO bisects ∠ A

In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and

1.	In an isosceles triangle ABC, with AB = AC, the bisectors of ∠ B and ∠ C intersect each other at O. Join A to O. Show that : (i) OB = OC (ii) AO bisects ∠ A
Answer» -step explanation:GIVEN:AB = AC andthe bisectors of B and C intersect each other at O(i) Since ABC is an ISOSCELES with AB = AC,B = C½ B = ½ C⇒ OBC = OCB (Angle bisectors)∴ OB = OC (Side opposite to the equal angles are equal.)(ii) In ΔAOB and ΔAOC,AB = AC (Given in the question)AO = AO (Common arm)OB = OC (As Proved Already)So, ΔAOB ΔAOC by SSS congruence condition.BAO = CAO (by CPCT)Thus, AO bisects A.