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Two parallel chords and a locus problem

Source: Turkey TST 1989 - P3

September 11, 2013

geometryperpendicular bisectorgeometry proposed

Problem Statement

Let

C_1

and

C_2

be given circles. Let

A_1

on

C_1

and

A_2

on

C_2

be fixed points. If chord

A_1P_1

of

C_1

is parallel to chord

A_2P_2

of

C_2

, find the locus of the midpoint of

P_1P_2

.

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