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Iberoamerican Olympiad 2013 - Problem 4

Source: http://oim2013.opm.org.pa/pdfs/examen_pt.pdf

August 13, 2014

geometryparallelogramgeometry proposed

Problem Statement

Let

\Gamma

be a circunference and

O

its center.

OE

is a diameter of

\Gamma

and

B

the midpoint of one of the arcs

AE

of

\Gamma

. The point

D \ne E

in on the segment

OE

. The point

C

is such that the quadrilateral

ABCD

is a parallelogram, with

AB

parallel to

CD

and

\Gamma

parallel to

AD

. The lines

EB

and

CD

meets at point

F

. The line

OF

cuts the minor arc

EB

of

\Gamma

at

I

.
Prove that the line

EI

is the angle bissector of

\angle BEC

.

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