Geometry Problem 1125:
Triangle, Four Equilateral Triangles, Centroid, Midpoint. Level: High School, SAT Prep,
Honors Geometry, College, Math Education
The figure below shows a triangle
ABC with equilateral triangles ABC1, BCA1,
and ACB1 of centroids C2, A2,
and B2, respectively. If A3, B3,
and C3 are the midpoints of AA2, BB2, and CC2,
respectively, prove that the triangle A3B3C3
is equilateral.