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National and Regional Contests
India Contests
Postal Coaching
2016 Postal Coaching
2016 Postal Coaching
Part of
Postal Coaching
Subcontests
(6)
6
2
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Subset of 63 points
Consider a set of
2016
2016
2016
distinct points in the plane, no four of which are collinear. Prove that there is a subset of
63
63
63
points among them such that no three of these
63
63
63
points are collinear.
Three lines meet - or actually, they don't
Let
K
K
K
and
L
L
L
be the centers of the excircles of a non-isosceles triangle
A
B
C
ABC
A
BC
opposite
B
B
B
and
C
C
C
respectively. Let
M
M
M
and
N
N
N
be points in the plane of the triangle such that
B
M
BM
BM
bisects
A
C
AC
A
C
and
C
N
CN
CN
bisects
A
B
AB
A
B
. Prove that the lines
K
M
KM
K
M
and
N
K
NK
N
K
meet on
B
C
BC
BC
.The problem in its current formulation is trivially wrong. No possible rectification is known to OP / was sent to the participants.
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