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TASIMO
2024 TASIMO
1
1
Part of
2024 TASIMO
Problems
(1)
Nice geometry problem about incenter
Source: 1st TASIMO, Day1 Problem1
5/18/2024
Let
A
B
C
ABC
A
BC
be a triangle with
A
B
<
A
C
AB<AC
A
B
<
A
C
and incenter
I
.
I.
I
.
A point
D
D
D
lies on segment
A
C
AC
A
C
such that
A
B
=
A
D
,
AB=AD,
A
B
=
A
D
,
and the line
B
I
BI
B
I
intersects
A
C
AC
A
C
at
E
.
E.
E
.
Suppose the line
C
I
CI
C
I
intersects
B
D
BD
B
D
at
F
,
F,
F
,
and
G
G
G
lies on segment
D
I
DI
D
I
such that
F
D
=
F
G
.
FD=FG.
F
D
=
FG
.
Prove that the lines
A
G
AG
A
G
and
E
F
EF
EF
intersect on the circumcircle of triangle
C
E
I
.
CEI.
CE
I
.
\\ Proposed by Avan Lim Zenn Ee, Malaysia
geometry
incenter