Question 39
Let $ABC$ be a triangle and let $X, Y, Z$ be interior points on the sides $BC, CA, AB$, respectively. Show that the magnified image of the triangle $XYZ$ under a homothety of factor $4$ from its centroid covers at least one of the vertices $A, B, C$.
Illustrative configuration with the three chosen side midpoints and centroid $G$; no generality is assumed from this particular drawing.
Illustrative configuration with the three chosen side midpoints and centroid $G$; no generality is assumed from this particular drawing.