# Woah what a ratio!!

Level pending

$$\triangle ABC$$ is an acute-angled triangle with $$AB=13$$ , $$BC=14$$ and $$AC=15$$. the circle $$\Gamma$$ with centre $$I$$ touches $$BC$$ at $$D$$ . Let $$AI$$ produced meet $$BC$$ at $$E$$ . Find the numerical value of $$\dfrac{[ABC]}{[ AID]-[IDE]}$$

$$[PQRS]$$ means area of the figure $$PQRS$$

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