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Problems
Contests
International Contests
Tournament Of Towns
1994 Tournament Of Towns
(418) 6
(418) 6
Part of
1994 Tournament Of Towns
Problems
(1)
collinearity from 1995 ToT
Source: TOT 418 1994 Spring A S6 - Tournament of Towns
6/12/2024
Consider a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
. Pairs of its opposite sides are continued until they intersect:
B
A
BA
B
A
and
C
D
CD
C
D
at the point
P
P
P
,
B
C
BC
BC
and
A
D
AD
A
D
at the point
Q
Q
Q
. Let
K
K
K
be the intersection point of the exterior bisectors of the angles
A
A
A
and
C
C
C
of the quadrilateral,
L
L
L
be the intersection point of the exterior bisectors of the angles
B
B
B
and
D
D
D
of the quadrilateral, and
M
M
M
be the intersection point of the exterior bisectors of the angles
P
P
P
and
Q
Q
Q
(the exterior bisector of an angle
X
X
X
is the line passing through X and perpendicular to its ordinary bisector). Prove that the points
K
K
K
,
L
L
L
and
M
M
M
lie on a straight line.(S Markelov)
geometry
collinear