1. In an isosceles triangle ABC; with AB = AC, the bisectors of LB and L C intersect each other at 0. Join A to 0. Show that: (i) OB = OC (ii) AO bisects LA.

(i ) In .'.\ ABC, AB = AC [Given] => LABC = LACB [Angles opposite to equal sides are equal.] BC 1 1 2 L ABC = 2 L ACB L OBC = L OCB => OC = OB [•: OB and OC are bisectors of LABC and LACB respectively.] ...(i) [Sides opposite to equal angles of a triangle are equal.] (ii) ) Consider triangles AOB and AOC, We have OC = OB [From (i)] AO = OA [Co:almon] TL.ES 75 and AB = AC A AOB ::A AOC [Given] [SSS rule]