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1992 Poland - First Round
5
5
Part of
1992 Poland - First Round
Problems
(1)
Halfplane
Source: Poland Math Olympiad 1992 First Round #5
6/2/2023
Given is a halfplane with points
A
A
A
and
C
C
C
on its edge. For every point
B
B
B
on this halfplane consider the squares
A
B
K
L
ABKL
A
B
K
L
and
B
C
M
N
BCMN
BCMN
lying outside the triangle
A
B
C
ABC
A
BC
. Prove that all the lines
L
M
LM
L
M
(as the point
B
B
B
varies) have a common point.