2001 IMO Shortlist Problems/G5
Problem
Let be an acute triangle. Let
, and
be isosceles triangles exterior to
, with
, and
, such that
![$\angle ADC = 2\angle BAC, \quad \angle BEA = 2 \angle ABC, \quad \angle CFB = 2 \angle ACB.$](http://latex.artofproblemsolving.com/d/4/8/d48fe472fcd1b014abe3c5c54ac815dee07f16f2.png)
Let be the intersection of lines
and
, let
be the intersection of
and
, and let
be the intersection of
and
. Find, with proof, the value of the sum
![$\frac {DB}{DD'} + \frac {EC}{EE'} + \frac {FA}{FF'}.$](http://latex.artofproblemsolving.com/c/d/b/cdbcc2213dd8d936d0be19e65bf8078571ffabbc.png)
Solution
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