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Problems
Contests
National and Regional Contests
Moldova Contests
Moldova Team Selection Test
1995 Moldova Team Selection Test
8
8
Part of
1995 Moldova Team Selection Test
Problems
(1)
Prove that points $M, N$ and $P$ are collinear.
Source: Moldova TST 1995
8/8/2023
Each pair of three circles have the common chords
A
A
1
,
B
B
1
AA_1, BB_1
A
A
1
,
B
B
1
and
C
C
1
CC_1{}
C
C
1
such that lines
A
B
AB{}
A
B
and
A
1
B
1
A_1B_1
A
1
B
1
intersect in point
M
M{}
M
,
B
C
BC
BC
and
B
1
C
1
B_1C_1
B
1
C
1
intersect in point
N
N{}
N
,
C
A
CA{}
C
A
and
C
1
A
1
C_1A_1
C
1
A
1
intersect in point
P
P{}
P
. Prove that points
M
,
N
M, N
M
,
N
and
P
P
P
are collinear.
geometry