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National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2010 Sharygin Geometry Olympiad
24
24
Part of
2010 Sharygin Geometry Olympiad
Problems
(1)
Find the locus of points Y (24)
Source:
10/29/2010
Let us have a line
ℓ
\ell
ℓ
in the space and a point
A
A
A
not lying on
ℓ
.
\ell.
ℓ
.
For an arbitrary line
ℓ
′
\ell'
ℓ
′
passing through
A
A
A
,
X
Y
XY
X
Y
(
Y
Y
Y
is on
ℓ
′
\ell'
ℓ
′
) is a common perpendicular to the lines
ℓ
\ell
ℓ
and
ℓ
′
.
\ell'.
ℓ
′
.
Find the locus of points
Y
.
Y.
Y
.
geometry unsolved
geometry