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Problems
Contests
International Contests
Cono Sur Olympiad
Cono Sur Shortlist - geometry
2009.G3
2009.G3
Part of
Cono Sur Shortlist - geometry
Problems
(1)
Convex polygon distances
Source:
11/26/2016
We have a convex polygon
P
P
P
in the plane and two points
S
,
T
S,T
S
,
T
in the boundary of
P
P
P
, dividing the perimeter in a proportion
1
:
2
1:2
1
:
2
. Three distinct points in the boundary, denoted by
A
,
B
,
C
A,B,C
A
,
B
,
C
start to move simultaneously along the boundary, in the same direction and with the same speed. Prove that there will be a moment in which one of the segments
A
B
,
B
C
,
C
A
AB, BC, CA
A
B
,
BC
,
C
A
will have a length smaller or equal than
S
T
ST
ST
.
geometry