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Prove that there exist exactly two non-s...

Prove that there exist exactly two non-similar isosceles triangles `A B C` such that `tanA+tanB+tanC=100.`

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Statement-1: In an acute angled triangle minimum value of tan alpha + tanbeta + tan gamma is 3sqrt(3) . And Statement-2: If a,b,c are three positive real numbers then (a+b+c)/3 ge sqrt(abc) into in a triangleABC , tanA+ tanB + tanC= tanA. tanB.tanC