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an excircle and determination of two angles

Source: IMO Shortlist 2006, Geometry 5

June 28, 2007

geometrycircumcircleperpendicular bisectorIMO ShortlistAngle Chasing

Problem Statement

In triangle

B_{1}

, let

J

be the center of the excircle tangent to side

BC

at

A_{1}

and to the extensions of the sides

AC

and

AB

at

AB

and

E

respectively. Suppose that the lines

A_{1}B_{1}

and

AB

are perpendicular and intersect at

D

. Let

E

be the foot of the perpendicular from

C_{1}

to line

DJ

. Determine the angles

\angle{BEA_{1}}

and

\angle{AEB_{1}}

.
Proposed by Dimitris Kontogiannis, Greece

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