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Prove that EI bisects <BEC

Source: Saudi Arabia IMO TST Day II Problem 1

July 22, 2014

geometry unsolvedgeometry

Problem Statement

Let

\Gamma

be a circle with center

O

and

AE

be a diameter. Point

D

lies on segment

OE

and point

B

is the midpoint of one of the arcs

\widehat{AE}

of

\Gamma

. Construct point

C

such that

ABCD

is a parallelogram. Lines

EB

and

CD

meet at

F

. Line

OF

meets the minor arc

\widehat{EB}

at

I

. Prove that

EI

bisects

\angle BEC

.

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