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All-Russian Olympiad
1981 All Soviet Union Mathematical Olympiad
305
305
Part of
1981 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 305 All Soviet Union MO 1981 perpendicular chords inside a cyclic
Source:
7/23/2019
Given points
A
,
B
,
M
,
N
A,B,M,N
A
,
B
,
M
,
N
on the circumference. Two chords
[
M
A
1
]
[MA_1]
[
M
A
1
]
and
[
M
A
2
]
[MA_2]
[
M
A
2
]
are orthogonal to lines
(
N
A
)
(NA)
(
N
A
)
and
(
N
B
)
(NB)
(
NB
)
respectively. Prove that
(
A
A
1
)
(AA_1)
(
A
A
1
)
and
(
B
B
1
)
(BB_1)
(
B
B
1
)
lines are parallel.
parallel
perpendicular
Cyclic