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Tournament Of Towns
1994 Tournament Of Towns
(426) 3
(426) 3
Part of
1994 Tournament Of Towns
Problems
(1)
equilateral wanted, started with intersection of 2 perp. lines with a circle
Source: TOT 426 1994 Autumn A J3 - Tournament of Towns
6/12/2024
Two-mutually perpendicular lines
ℓ
\ell
ℓ
and
m
m
m
intersect each other at a point of the circumference of a circle, dividing it into three arcs. A point
M
i
M_i
M
i
(
i
=
1
i = 1
i
=
1
,
2
2
2
,
3
3
3
) is taken on each arc so that the tangent line to the circumference at the point
M
i
M_i
M
i
intersects
ℓ
\ell
ℓ
and
m
m
m
in two points at the same distance from
M
i
M_i
M
i
(that is
M
i
M_i
M
i
is the midpoint of the segment between them). Prove that the triangle
M
1
M
2
M
3
M_1M_2M_3
M
1
M
2
M
3
is equilateral. (Przhevalsky)
geometry
Equilateral