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AT // BC wanted

Source: IMO 2019 SL G1

September 22, 2020

geometryIMO Shortlist

Problem Statement

Let

BC

be a triangle. Circle

\Gamma

passes through

A

, meets segments

AB

and

AC

again at points

D

and

E

respectively, and intersects segment

BC

at

F

and

G

such that

F

lies between

B

and

G

. The tangent to circle

BDF

at

F

and the tangent to circle

CEG

at

G

meet at point

T

. Suppose that points

A

and

T

are distinct. Prove that line

AT

is parallel to

BC

.
(Nigeria)

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