MathDB

Consider the equilateral triangle

ABC

with center of gravity

G

. Let

M

be a point, inside the triangle and

O

be the midpoint of the segment

MG

. Three segments go through

M

, each parallel to one side of the triangle and with the ends on the other two sides of the given triangle.
a) Show that

O

is at equal distances from the midpoints of the three segments considered. b) Show that the midpoints of the three segments are the vertices of an equilateral triangle.

Problem Statement