MathDB

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'}.

Problem Statement