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IMO ShortList 2002, geometry problem 8

Source: IMO ShortList 2002, geometry problem 8

September 28, 2004

geometrycirclesright angleIMO Shortlist

Problem Statement

Let two circles

S_{1}

and

S_{2}

meet at the points

A

and

B

. A line through

A

meets

S_{1}

again at

C

and

S_{2}

again at

D

. Let

M

,

N

,

K

be three points on the line segments

CD

,

F

,

BD

respectively, with

MN

parallel to

BD

and

MK

parallel to

BC

. Let

E

and

F

be points on those arcs

BC

of

S_{1}

and

BD

of

S_{2}

respectively that do not contain

A

. Given that

EN

is perpendicular to

BC

and

FK

is perpendicular to

BD

prove that

\angle EMF=90^{\circ}

.

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