triangle is equilateral if and only if any three of the smaller triangles have either the same perimeter or the same inradius. A triangle is equilateral if and only if the circumcenters of any three of the smaller triangles have the same distance from the centroid.
Because a equilateral triangle has 3 equal angles. The 3 angle of a triangle equal 180°. So if the angles are equal in an equilateral triangle, we do 60° times 3 which equal 180°.
