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Serbia Junior Balkan TST 2015

Source:

May 25, 2015

geometry

Problem Statement

The diagonals

AD

,

BE

,

CF

of cyclic hexagon

ABCDEF

intersect in

S

and

AB

is parallel to

CF

and lines

DE

and

CF

intersect each other in

M

. Let

N

be a point such that

M

is the midpoint of

SN

. Prove that circumcircle of

\triangle ADN

is passing through midpoint of segment

CF

.

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