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Macedonian JBMO TST 2009 - Problem 3

Source: Macedonian JBMO TST

September 23, 2012

geometry proposedgeometry

Problem Statement

Let

\triangle ABC

be equilateral. On the side

AB

points

C_{1}

and

C_{2}

, on the side

AC

points

B_{1}

and

B_{2}

are chosen, and on the side

BC

points

A_{1}

and

A_{2}

are chosen. The following condition is given :

A_{1}A_{2}

=

B_{1}B_{2}

=

C_{1}C_{2}

. Let the intersection lines

A_{2}B_{1}

and

B_{2}C_{1}

,

B_{2}C_{1}

and

C_{2}A_{1}

and

C_{2}A_{1}

and

A_{2}B_{1}

are

E

,

F

, and

G

respectively. Show that the triangle formed by

B_{1}A_{2}

,

A_{1}C_{2}

and

C_{1}B_{2}

is similar to

\triangle EFG

.

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