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Sweden Contests
Swedish Mathematical Competition
1979 Swedish Mathematical Competition
6
6
Part of
1979 Swedish Mathematical Competition
Problems
(1)
aAB < AG < b AB and c AB < BG < d AB if G centroid , G and GA > GB > GC
Source: 1979 Swedish Mathematical Competition p6
3/26/2021
Find the sharpest inequalities of the form
a
⋅
A
B
<
A
G
<
b
⋅
A
B
a\cdot AB < AG < b\cdot AB
a
⋅
A
B
<
A
G
<
b
⋅
A
B
and
c
⋅
A
B
<
B
G
<
d
⋅
A
B
c\cdot AB < BG < d\cdot AB
c
⋅
A
B
<
BG
<
d
⋅
A
B
for all triangles
A
B
C
ABC
A
BC
with centroid
G
G
G
such that
G
A
>
G
B
>
G
C
GA > GB > GC
G
A
>
GB
>
GC
.
Geometric Inequalities
geometry
Centroid