MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Sharygin Geometry Olympiad
2006 Sharygin Geometry Olympiad
17
17
Part of
2006 Sharygin Geometry Olympiad
Problems
(1)
intersecting circles, parallel chords, intersections, parallel wanted
Source: Sharygin 2006 IX-XI CR 17
8/24/2019
In two circles intersecting at points
A
A
A
and
B
B
B
, parallel chords
A
1
B
1
A_1B_1
A
1
B
1
and
A
2
B
2
A_2B_2
A
2
B
2
are drawn. The lines
A
A
1
AA_1
A
A
1
and
B
B
2
BB_2
B
B
2
intersect at the point
X
,
A
A
2
X, AA_2
X
,
A
A
2
and
B
B
1
BB_1
B
B
1
intersect at the point
Y
Y
Y
. Prove that
X
Y
/
/
A
1
B
1
XY // A_1B_1
X
Y
//
A
1
B
1
.
circles
geometry
parallel