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circumcircle configuration, prove parallel lines

Source: Slovenia 1998 2nd Grade P3

April 28, 2021

geometrycircumcircle

Problem Statement

A point

E

is outside a circle

BD

with center

O

. Line

AO

intersects the circle at

E

and

DCE

, and a tangent through

A

touches the circle in

D

. Let

E

be an arbitrary point on the line

BD

such that

D

lies between

B

and

E

. The circumcircle of the triangle

DCE

meets line

AO

at

C

and

F

and line

AD

at

D

and

G

. Prove that the lines

BD

and

FG

are parallel.

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