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Turkey TST Triangle Inequality

Source: Turkey TST 2009, Problem 5

April 5, 2009
inequalitiesgeometrygeometry unsolved

Problem Statement

In a triangle ABC ABC incircle touches the sides AB AB, AC AC and BC BC at C1 C_1, B1 B_1 and A1 A_1 respectively. Prove that \sqrt {\frac {AB_1}{AB}} \plus{} \sqrt {\frac {BC_1}{BC}} \plus{} \sqrt {\frac {CA_1}{CA}}\leq\frac {3}{\sqrt {2}} is true.
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