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National and Regional Contests
Serbia Contests
Serbia JBMO TST
2018 Serbia JBMO TST
1
1
Part of
2018 Serbia JBMO TST
Problems
(1)
Three collinear points
Source: Serbian JBMO TST 2018, problem 1
5/21/2018
Let
A
D
AD
A
D
be an internal angle bisector in triangle
Δ
A
B
C
\Delta ABC
Δ
A
BC
. An arbitrary point
M
M
M
is chosen on the closed segment
A
D
AD
A
D
. A parallel to
B
C
BC
BC
through
M
M
M
cuts
A
B
AB
A
B
at
N
N
N
. Let
A
D
,
C
M
AD, CM
A
D
,
CM
cut circumcircle of
Δ
A
B
C
\Delta ABC
Δ
A
BC
at
K
,
L
K, L
K
,
L
, respectively. Prove that
K
,
N
,
L
K,N,L
K
,
N
,
L
are collinear.
geometry