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2023 APMO
3
3
Part of
2023 APMO
Problems
(1)
APMO 2023 Problem 3
Source:
7/5/2023
Let
A
B
C
D
ABCD
A
BC
D
be a parallelogram. Let
W
,
X
,
Y
,
W, X, Y,
W
,
X
,
Y
,
and
Z
Z
Z
be points on sides
A
B
,
B
C
,
C
D
,
AB, BC, CD,
A
B
,
BC
,
C
D
,
and
D
A
DA
D
A
, respectively, such that the incenters of triangles
A
W
Z
,
B
X
W
,
C
Y
X
,
AWZ, BXW, CYX,
A
W
Z
,
BX
W
,
C
Y
X
,
and
D
Z
Y
DZY
D
Z
Y
form a parallelogram. Prove that
W
X
Y
Z
WXYZ
W
X
Y
Z
is a parallelogram.
APMO
APMO 2023
geometry