Τρίτη, 17 Οκτωβρίου 2017

2001 IMO Shortlist G5

Let $ABC$ be an acute triangle. Let $DAC,EAB$, and $FBC$ be isosceles triangles exterior to $ABC$, with$ DA = DC,EA = EB$, and $FB = FC$, such that $\angle ADC = 2\angle BAC, \angle BEA = 2\angle ABC, \angle CFB = 2\angle ACB$. Let $D’$ be the intersection of lines $DB$ and $EF$, let $E’$ be the intersection of $EC$ and $DF$, and let $F’$ be the intersection of $FA$ and $DE$. Find, with proof, the value of the sum $\frac{DB}{DD’} +\frac{EC}{EE’} +\frac{FA}{FF’}$ .

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