IMO Shortlist 1966 problem 17


Kvaliteta:
  Avg: 0,0
Težina:
  Avg: 0,0
Dodao/la: arhiva
2. travnja 2012.
LaTeX PDF
Let ABCD and A^{\prime }B^{\prime}C^{\prime }D^{\prime } be two arbitrary parallelograms in the space, and let M, N, P, Q be points dividing the segments AA^{\prime }, BB^{\prime }, CC^{\prime }, DD^{\prime } in equal ratios.

a.) Prove that the quadrilateral MNPQ is a parallelogram.

b.) What is the locus of the center of the parallelogram MNPQ, when the point M moves on the segment AA^{\prime } ?

(Consecutive vertices of the parallelograms are labelled in alphabetical order.
Izvor: Međunarodna matematička olimpijada, shortlist 1966