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2021-IMOC qualification
G2
G2
Part of
2021-IMOC qualification
Problems
(1)
DE _|_AC if DF _|_ AB
Source: 2021 IMOC qualification problem, G2
12/30/2021
Given a triangle
A
B
C
ABC
A
BC
,
D
D
D
is the reflection from the perpendicular foot from
A
A
A
to
B
C
BC
BC
through the midpoint of
B
C
BC
BC
.
E
E
E
is the reflection from the perpendicular foot from
B
B
B
to
C
A
CA
C
A
through the midpoint of
C
A
CA
C
A
.
F
F
F
is the reflection from the perpendicular foot from
C
C
C
to
A
B
AB
A
B
through the midpoint of
A
B
AB
A
B
. Prove:
D
E
⊥
A
C
DE \perp AC
D
E
⊥
A
C
if and only if
D
F
⊥
A
B
DF \perp AB
D
F
⊥
A
B
geometry
perpendicular