Problem

Source: VII International Festival of Young Mathematicians Sozopol 2016, Theme for 10-12 grade

Tags: geometry, area of a triangle



Circle $k$ passes through $A$ and intersects the sides of $\Delta ABC$ in $P,Q$, and $L$. Prove that: $\frac{S_{PQL}}{S_{ABC}}\leq \frac{1}{4} (\frac{PL}{AQ})^2$.


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