MathDB
Nice problem from a friend: prove G is the centroid of ABP

Source: Central American Olympiad 2007, Problem 6

June 12, 2007
geometryparallelogramincenterperpendicular bisectorgeometry proposed

Problem Statement

Consider a circle SS, and a point PP outside it. The tangent lines from PP meet SS at AA and BB, respectively. Let MM be the midpoint of ABAB. The perpendicular bisector of AMAM meets SS in a point CC lying inside the triangle ABPABP. ACAC intersects PMPM at GG, and PMPM meets SS in a point DD lying outside the triangle ABPABP. If BDBD is parallel to ACAC, show that GG is the centroid of the triangle ABPABP. Arnoldo Aguilar (El Salvador)
Back to ProblemsView on AoPS