MathDB
Intersection set of circles

Source: Turkey NMO 2008 Problem 5

December 2, 2008
geometrysymmetrygeometry unsolved

Problem Statement

A circle Γ \Gamma and a line \ell is given in a plane such that \ell doesn't cut Γ \Gamma.Determine the intersection set of the circles has [AB] [AB] as diameter for all pairs of {A,B} \left\{A,B\right\} (lie on \ell) and satisfy P,Q,R,SΓ P,Q,R,S \in \Gamma such that PQ \cap RS\equal{}\left\{A\right\} and PS \cap QR\equal{}\left\{B\right\}