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All-Russian Olympiad
1986 All Soviet Union Mathematical Olympiad
428
428
Part of
1986 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 428 All Soviet Union MO 1986 equal angles impossible
Source:
8/6/2019
A line is drawn through the
A
A
A
vertex of triangle
A
B
C
ABC
A
BC
with
∣
A
B
∣
≠
∣
A
C
∣
|AB|\ne|AC|
∣
A
B
∣
=
∣
A
C
∣
. Prove that the line can not contain more than one point
M
M
M
such, that
M
M
M
is not a triangle vertex, and
∠
A
B
M
=
∠
A
C
M
\angle ABM = \angle ACM
∠
A
BM
=
∠
A
CM
. What lines do not contain such a point
M
M
M
at all?
geometry
equal angles
Line