Problem 1:
Given an arbitrary triangle $ABC$ with area $T$ and perimeter $L$. Let $P,Q,R$ be the points of tangency of the sides $BC,CA,AB$ respectively with the inscribed circle. Prove that \[ \left ( \frac{AB}{PQ} \right )^3+ \left ( \frac{BC}{QR} \right )^3+\left ( \frac{CA}{RP} \right )^3 \geq \frac{2}{\sqrt{3}}\cdot \frac{L^2}{T}\]
Bangladesh IMO TST 1: 2011/ Geometry-2 (P 1)
"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin
Please install LaTeX fonts in your PC for better looking equations,
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Please install LaTeX fonts in your PC for better looking equations,
learn how to write equations, and don't forget to read Forum Guide and Rules.