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International Contests
Baltic Way
2019 Baltic Way
12
12
Part of
2019 Baltic Way
Problems
(1)
Floating orthocenter forms an if and only if condition
Source: 2019 Baltic Way P12
11/18/2019
Let
A
B
C
ABC
A
BC
be a triangle and
H
H
H
its orthocenter. Let
D
D
D
be a point lying on the segment
A
C
AC
A
C
and let
E
E
E
be the point on the line
B
C
BC
BC
such that
B
C
⊥
D
E
BC\perp DE
BC
⊥
D
E
. Prove that
E
H
⊥
B
D
EH\perp BD
E
H
⊥
B
D
if and only if
B
D
BD
B
D
bisects
A
E
AE
A
E
.
geometry