5.2.5.2 Locus of points

Condition: Given a line \( m \) and a point \( P \) outside the line. All possible triangles \( A B C \) are constructed in which the vertices \( A \) and \( B \) lie on the line \( m \), and the intersection point of the medians coincides with the point P. Find the set of all positions of the point \( C \).