We have indicated the source of these problems.

Do not look up solutions. It is fun to try it yourself or see others try them live!

  1. Let P be an interior point of triangle ABC and AP, BP, CP meet the sides BC, CA, AB in D, E, F respectively. Show that \( \frac{AP}{PD}=\frac{AF}{FB}+\frac{AE}{EC} \)   (RMO 1991, #1, India)
  2. Determine the set of integers n for which \( n^2+19n+92 \) is a square of an integer. (RMO 1992, #1, India)
  3. Let ABC be an acute-angled triangle and CD be the altitude through C. If AB = 8 and CD = 6, find the distance between the mid-points of AD and BC. (RMO 1993, #1, India)

Apart from these problems, the Problem Solving Sessions at Cheenta is also an opportunity to discuss your doubts.