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Prove that AC + CF = AB + BF

Source:

September 1, 2010

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Problem Statement

Points

CD

and

E

are chosen on the sides

AB

and

AC

of the triangle

ABC

in such a way that if

F

is the intersection point of

BE

and

CD

, then

AE + EF = AD + DF

. Prove that

AC + CF = AB + BF.

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