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Contests
National and Regional Contests
Turkey Contests
Turkey Team Selection Test
1989 Turkey Team Selection Test
3
3
Part of
1989 Turkey Team Selection Test
Problems
(1)
Two parallel chords and a locus problem
Source: Turkey TST 1989 - P3
9/11/2013
Let
C
1
C_1
C
1
and
C
2
C_2
C
2
be given circles. Let
A
1
A_1
A
1
on
C
1
C_1
C
1
and
A
2
A_2
A
2
on
C
2
C_2
C
2
be fixed points. If chord
A
1
P
1
A_1P_1
A
1
P
1
of
C
1
C_1
C
1
is parallel to chord
A
2
P
2
A_2P_2
A
2
P
2
of
C
2
C_2
C
2
, find the locus of the midpoint of
P
1
P
2
P_1P_2
P
1
P
2
.
geometry
perpendicular bisector
geometry proposed