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Problems
Contests
National and Regional Contests
Cuba Contests
Cuba MO
2008 Cuba MO
8
8
Part of
2008 Cuba MO
Problems
(1)
locus of centers of rectangles inscribed in acute triangle
Source: 2008 Cuba MO 2.8
8/27/2024
Let
A
B
C
ABC
A
BC
an acute-angle triangle. Let
R
R
R
be a rectangle with vertices in the edges of
A
B
C
ABC
A
BC
. Let
O
O
O
be the center of
R
R
R
. a) Find the locus of all the points
O
O
O
. b) Decide if there is a point that is the center of three of these rectangles.
geometry
rectangle
Locus