# Is it possible to reconstruct a triangle from the midpoints of its sides?

Take $ABC$ an arbitrary triangle, it is easy to take the midpoints $P$, $Q$, $R$ of sides $AB$, $BC$, $CA$, and we all know that the medians $CP$, $AQ$, $BR$ intersect at a point called the centroid (or barycenter) of the triangle.

But, given three points $P$, $Q$, $R$, is it possible, using tools of Euclidean geometry, to reconstruct the triangle (or one of the triangles, if there are many) of which they are the midpoints of sides?

• Yes, and that triangle would be unique! – Emo Feb 20 '14 at 12:51