The Total solution for NCERT class 6-12
In an isosceles triangle ABC, with AB = AC, the bisectorsof ∠B and ∠C intersect each other at O. Join A to O.Show that:
(i) OB = OC (ii) AO bisects ∠A
(i) It is given that in triangle ABC, AB = AC
⇒ ∠ACB = ∠ABC (Angles opposite to equal sides of atriangle are equal)
⇒ ∠OCB = ∠OBC
⇒ OB = OC (Sides opposite to equal angles of a triangle arealso equal)
(ii) In ΔOAB and ΔOAC,
AO =AO (Common)
AB = AC (Given)
OB = OC (Proved above)
Therefore, ΔOAB ≅ ΔOAC (BySSS congruence rule)
⇒ ∠BAO = ∠CAO (CPCT)