Question

If triangle ABC is isosceles with AB=AC and C(O,r) is the incircle of the triangle ABC touching BC at L ,prove that L bisects BC

Answer 1

Solution: In the Triangle ABC, AB=BC, therefore, ½ <C= ½<B, => <OCI=<OBI (since, OB bisects angle B and OC angle C).

In the triangle, OBI and OCI, <OIB=<OIC (radius is always perpendicular to the circle’s tangent), <OCI=<OBI (proved earlier), OI=OI (Common).

Hence, given triangles are congruent through AAS. Hence, BI=CI (by CPCT) or I bisect line BC.

Answer 2

Answer: PROVED BELOW

Explanation: