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There exists a point M depending on C1, C2 [Spain 2000]

Source:

February 3, 2011

geometrygeometric transformationreflectionperpendicular bisectorgeometry unsolved

Problem Statement

Two circles

C_1

and

C_2

with the respective radii

r_1

and

r_2

intersect in

A

and

B.

A variable line

r

through

B

meets

C_1

and

C_2

again at

P_r

and

Q_r

respectively. Prove that there exists a point

M,

depending only on

C_1

and

C_2,

such that the perpendicular bisector of each segment

P_rQ_r

passes through

M.