A $ABC$ triangle divide by a $d$ line such that, new two pieces' areas are equal. $d$ line intersects with $[AB]$ at $D$, $[AC]$ at $E$. Prove that $$\frac{AD+AE}{BD+DE+EC+CB} > \frac{1}{4}$$
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Tags: geometric inequality, geometry
A $ABC$ triangle divide by a $d$ line such that, new two pieces' areas are equal. $d$ line intersects with $[AB]$ at $D$, $[AC]$ at $E$. Prove that $$\frac{AD+AE}{BD+DE+EC+CB} > \frac{1}{4}$$