It is easy to construct one equilateral triangle from three identical matches. Can we make four equilateral triangles by adding just three more matches identical to the original ones?
Two segments \(AB\) and \(A'B'\) are given on a plane. Construct the point \(O\) so that the triangles \(AOB\) and \(A'OB'\) are similar (the same letters denote the corresponding vertices of similar triangles).