MathDB
Problems
Contests
International Contests
IMO Shortlist
2019 IMO Shortlist
G1
G1
Part of
2019 IMO Shortlist
Problems
(1)
AT // BC wanted
Source: IMO 2019 SL G1
9/22/2020
Let
A
B
C
ABC
A
BC
be a triangle. Circle
Γ
\Gamma
Γ
passes through
A
A
A
, meets segments
A
B
AB
A
B
and
A
C
AC
A
C
again at points
D
D
D
and
E
E
E
respectively, and intersects segment
B
C
BC
BC
at
F
F
F
and
G
G
G
such that
F
F
F
lies between
B
B
B
and
G
G
G
. The tangent to circle
B
D
F
BDF
B
D
F
at
F
F
F
and the tangent to circle
C
E
G
CEG
CEG
at
G
G
G
meet at point
T
T
T
. Suppose that points
A
A
A
and
T
T
T
are distinct. Prove that line
A
T
AT
A
T
is parallel to
B
C
BC
BC
.(Nigeria)
geometry
IMO Shortlist