RMO Delhi Q.1
Source:
December 31, 2015
Problem Statement
2 circles Γ and Σ, with centers O and P, respectively, are such that P lies on Γ. Let A be a point on Σ, and let M be the midpoint of AP. Let B be another point on Σ, such that AB||OM. Then prove that the midpoint of AB lies on Γ.