IMO 2014 Shortlist G4
Consider a fixed circle Γ with three fixed points A, B, and C on it. Also, let us fix a real number λ P p0,1q. For a var...
Category: Geometry
Problem
Consider a fixed circle Γ with three fixed points A, B, and C on it. Also, let us fix a real number λ P p0,1q. For a variable point P R tA,B,Cu on Γ, let M be the point on the segment CP such that CM “ λ ¨ CP. Let Q be the second point of intersection of the circumcircles of the triangles AMP and BMC. Prove that as P varies, the point Q lies on a fixed circle. (United Kingdom)