# A problem by Sagnik Saha

Level pending

$$\triangle ABC$$ is an acute-angled triangle with $$AB=13$$ , $$BC=14$$ and $$AC=15$$. The incircle $$\Gamma$$ of $$ABC$$ with centre $$I$$ touches $$BC$$ at $$D$$ . Let $$AI$$ produced meet $$BC$$ at $$E$$ . Let $$K$$ be the mid-point of $$BC$$. $$KI$$ meets $$AD$$ at $$L$$. Find the numerical value of

$\dfrac{[R_1] \times [R_2] \times [R_3]}{[ABC]-\frac{4}{3}[LDK]}.$

Details and assumptions

$$R_1$$ is the circumradius of $$\triangle ABC$$, $$R_2$$ is the circumradius of $$\triangle ALI$$ , $$R_3$$ is the circumradius of $$\triangle IDE$$

$$[PQRS]$$ denotes the area of the figure $$PQRS$$.

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