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Problems
Contests
International Contests
Tournament Of Towns
1991 Tournament Of Towns
(295) 2
(295) 2
Part of
1991 Tournament Of Towns
Problems
(1)
TOT 295 1991 Spring A S2 fixed point for lines
Source:
6/9/2024
The chord
M
N
MN
MN
on the circle is fixed. For every diameter
A
B
AB
A
B
of the circle consider the intersection point
C
C
C
of the lines
A
M
AM
A
M
and
B
N
BN
BN
and construct the line
ℓ
\ell
ℓ
passing through
C
C
C
perpendicularly to
A
B
AB
A
B
. Prove that all the lines
ℓ
\ell
ℓ
pass through a fixed point.(E. Kulanin, Moscow)
geometry
fixed
Fixed point