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Problems of the week (December 18 to 24)

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.

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