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Sharygin Geometry Olympiad
2006 Sharygin Geometry Olympiad
13
13
Part of
2006 Sharygin Geometry Olympiad
Problems
(1)
2 fixed lines and 2 fixed points, 2 parallel segments, locus of intersection
Source: Sharygin 2006 IX- X CR 13
8/23/2019
Two straight lines
a
a
a
and
b
b
b
are given and also points
A
A
A
and
B
B
B
. Point
X
X
X
slides along the line
a
a
a
, and point
Y
Y
Y
slides along the line
b
b
b
, so that
A
X
∥
B
Y
AX \parallel BY
A
X
∥
B
Y
. Find the locus of the intersection point of
A
Y
AY
A
Y
with
X
B
XB
XB
.
Locus
geometry
Locus problems
lines
parallel