TR-MO 2005 Problem 5

Kenar uzunlukları $a, b, c$ ve iç teğet çemberinin yarıçapı $r$ olan bir üçgende, $\frac{1}{a^2} + \frac{1}{b^2} + \frac{1}{c^2} \le \frac{1}{4r^2}$ olduğunu gösteriniz.

Official text Turkish Mathematical Olympiad 2005 official paper, page 2. Quoted with source.

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