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locus of centroids of triangles, 2 vertices on one circle, 3rd on another

Source: 2006 Oral Moscow Geometry Olympiad grades 10-11 p3

October 20, 2020

geometryLocusCentroid

Problem Statement

Two non-rolling circles

C_1

and

C_2

with centers

O_1

and

O_2

and radii

2R

and

R

, respectively, are given on the plane. Find the locus of the centers of gravity of triangles in which one vertex lies on

C_1

and the other two lie on

C_2

.
(B. Frenkin)