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International Contests
Tournament Of Towns
1993 Tournament Of Towns
(390) 2
(390) 2
Part of
1993 Tournament Of Towns
Problems
(1)
TOT 390 1993 Autumn O S2 <MCN =45^o , BC = BM, AC = AN, right triangle
Source:
6/12/2024
Points
M
M
M
and
N
N
N
are taken on the hypotenuse
A
B
AB
A
B
of a right triangle
A
B
C
ABC
A
BC
so that
B
C
=
B
M
BC = BM
BC
=
BM
and
A
C
=
A
N
AC = AN
A
C
=
A
N
. Prove that the angle
M
C
N
MCN
MCN
is equal to
45
45
45
degrees. (Folklore)
geometry
angles
right triangle