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International Contests
Tournament Of Towns
1993 Tournament Of Towns
(370) 2
(370) 2
Part of
1993 Tournament Of Towns
Problems
(1)
CM = CN if BM = DN for cyclic ABCD
Source: TOT 370 1993 Spring O S2 - Tournament of Towns
6/10/2024
Quadrilateral
A
B
C
D
ABCD
A
BC
D
is inscribed in a circle,
M
M
M
is the intersection point of the lines
A
B
AB
A
B
and
C
D
CD
C
D
and
N
N
N
is the intersection point of the lines
B
C
BC
BC
and
A
D
AD
A
D
. It is known that
B
M
=
D
N
BM = DN
BM
=
D
N
. Prove that
C
M
=
C
N
CM = CN
CM
=
CN
. (F Nazarov)
geometry
cyclic quadrilateral
equal segments