Problem

Source: Turkey TST 2009, Problem 5

Tags: inequalities, geometry, geometry unsolved



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