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Some fixed point

Source: Greek national M.O. 2004, Final Round,problem 3

November 15, 2011

symmetrygeometry unsolvedgeometry

Problem Statement

Consider a circle

K(O,r)

and a point

A

outside

K.

A line

\epsilon

different from

AO

cuts

K

at

B

and

C,

where

B

lies between

A

and

C.

Now the symmetric line of

\epsilon

with respect to axis of symmetry the line

AO

cuts

K

at

E

and

D,

where

E

lies between

A

and

D.

Show that the diagonals of the quadrilateral

BCDE

intersect in a fixed point.

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