MathDB

Macedonia National Olympiad 2011 - Problem 2

Source:

April 16, 2011

greatest common divisorgeometrycircumcircleincentertrigonometrysymmetryfunction

Problem Statement

Acute-angled

~

\triangle{ABC}

~

is given. A line

~

l

~

parallel to side

~

AB

~

passing through vertex

~

C

~

is drawn. Let the angle bisectors of

~

\angle{BAC}

~

and

~

\angle{ABC}

~

intersect the sides

~

BC

and

~

AC

at points

~

D

~

and

~

F

, and line

~

l

~

at points

~

E

~

and

~

G

~

respectively. Prove that if

~

\overline{DE}=\overline{GF}

~

then

~

\overline{AC}=\overline{BC}\, .

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