MathDB
Problems
Contests
International Contests
CentroAmerican
2002 CentroAmerican
2
2
Part of
2002 CentroAmerican
Problems
(1)
Triangles
Source: Central American Olympiad 2002, problem 2
12/30/2009
Let
A
B
C
ABC
A
BC
be an acute triangle, and let
D
D
D
and
E
E
E
be the feet of the altitudes drawn from vertexes
A
A
A
and
B
B
B
, respectively. Show that if,
A
r
e
a
[
B
D
E
]
≤
A
r
e
a
[
D
E
A
]
≤
A
r
e
a
[
E
A
B
]
≤
A
r
e
a
[
A
B
D
]
Area[BDE]\le Area[DEA]\le Area[EAB]\le Area[ABD]
A
re
a
[
B
D
E
]
≤
A
re
a
[
D
E
A
]
≤
A
re
a
[
E
A
B
]
≤
A
re
a
[
A
B
D
]
then, the triangle is isosceles.
geometry