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Balkan MO
1999 Balkan MO
3
3
Part of
1999 Balkan MO
Problems
(1)
ABC is an acute-angled triangle with area 1
Source: Balkan MO 1999, Problem 3
4/24/2006
Let
A
B
C
ABC
A
BC
be an acute-angled triangle of area 1. Show that the triangle whose vertices are the feet of the perpendiculars from the centroid
G
G
G
to
A
B
AB
A
B
,
B
C
BC
BC
,
C
A
CA
C
A
has area between
4
27
\frac 4{27}
27
4
and
1
4
\frac 14
4
1
.
geometry
inequalities
trigonometry
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