2001 IMO Shortlist Problems/G5

Revision as of 18:47, 20 August 2008 by Minsoens (talk | contribs) (New page: == Problem == Let <math>ABC</math> be an acute triangle. Let <math>DAC,EAB</math>, and <math>FBC</math> be isosceles triangles exterior to <math>ABC</math>, with <math>DA = DC, EA = EB</m...)
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Problem

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

$\angle ADC = 2\angle BAC, \quad \angle BEA = 2 \angle ABC, \quad \angle CFB = 2 \angle ACB.$

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

$\frac {DB}{DD'} + \frac {EC}{EE'} + \frac {FA}{FF'}.$

Solution

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