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Japan MO Finals
2023 Japan MO Finals
2
2
Part of
2023 Japan MO Finals
Problems
(1)
Standard geo
Source: 2023 Japan MO Finals 2
2/11/2023
In an acute triangle
A
B
C
ABC
A
BC
, let
D
,
E
,
F
D,E,F
D
,
E
,
F
be the midpoints of
B
C
,
C
A
,
A
B
BC,CA,AB
BC
,
C
A
,
A
B
respectively. Let
X
,
Y
X,Y
X
,
Y
be the feet of altitude from
D
D
D
to
A
B
,
A
C
AB,AC
A
B
,
A
C
respectively. The line through
F
F
F
parallel to
X
Y
XY
X
Y
meets line
D
Y
DY
D
Y
at
P
P
P
. Prove that
A
D
⊥
E
P
AD\perp EP
A
D
⊥
EP
.
geometry