MathDB
two intersecting spheres

Source: Sharygin contest 2008. The correspondence round. Problem 23

September 3, 2008
geometry3D geometryspheregeometry proposed

Problem Statement

(V.Protasov, 10--11) In the space, given two intersecting spheres of different radii and a point A A belonging to both spheres. Prove that there is a point B B in the space with the following property: if an arbitrary circle passes through points A A and B B then the second points of its meet with the given spheres are equidistant from B B.