More problems

Problem 1. (Pappus's theorem) If A, C and E are three points on one line, B, D and F on another, and if the three lines AB, CD and EF meet DE, FA and BC, respectively, then the three points of intersection L, M and N are collinear.

Hint. Use the Menelaus's theorem for the five triples of points LDE, AMF, BCN, ACE and BDF on the sides of the triangle UVW formed by the lines AB, CD and EF (see Figure 6).

  

Figure 6: Pappus's theorem