MathDB
Problems
Contests
National and Regional Contests
India Contests
India Pre-Regional Mathematical Olympiad
2018 India PRMO
21
21
Part of
2018 India PRMO
Problems
(1)
PRMO 2018
Source: Pre-RMO India
8/25/2018
Let
Δ
A
B
C
\Delta ABC
Δ
A
BC
be an acute-angled triangle and let
H
H
H
be its orthocentre. Let
G
1
,
G
2
G_1, G_2
G
1
,
G
2
and
G
3
G_3
G
3
be the centroids of the triangles
Δ
H
B
C
,
Δ
H
C
A
\Delta HBC , \Delta HCA
Δ
H
BC
,
Δ
H
C
A
and
Δ
H
A
B
\Delta HAB
Δ
H
A
B
respectively. If the area of
Δ
G
1
G
2
G
3
\Delta G_1G_2G_3
Δ
G
1
G
2
G
3
is
7
7
7
units, what is the area of
Δ
A
B
C
\Delta ABC
Δ
A
BC
?
geometry
orthocenter
median