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Austrian-Polish
1997 Austrian-Polish Competition
4
4
Part of
1997 Austrian-Polish Competition
Problems
(1)
midpoint of orthocenters, trapezoid- Austrian-Polish 1997, 2003 Rioplatense L1p2
Source:
5/19/2019
In a trapezoid
A
B
C
D
ABCD
A
BC
D
with
A
B
/
/
C
D
AB // CD
A
B
//
C
D
, the diagonals
A
C
AC
A
C
and
B
D
BD
B
D
intersect at point
E
E
E
. Let
F
F
F
and
G
G
G
be the orthocenters of the triangles
E
B
C
EBC
EBC
and
E
A
D
EAD
E
A
D
. Prove that the midpoint of
G
F
GF
GF
lies on the perpendicular from
E
E
E
to
A
B
AB
A
B
.
geometry
trapezoid
orthocenter
midpoint