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
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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.
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Answer: PROVED BELOW
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