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Problem of the Week

Problem 6 (due Monday, April 22)

Let $ABCD$ be a convex quadrilateral whose diagonals $AC$ and $BD$ intersect at a point P. Let $M,N$ be the midpoints of the sides $AB$ and $CD$ respectively. Prove that the area of the triangle $PMN$ is equal to the quarter of the absolute value of the difference between the area of the triangle $DAP$ and the area of the triangle $BCP$: \[ \text{area}(\triangle MNP)=\frac{1}{4}\left|\text{area}(\triangle DAP)-\text{area}(\triangle BCP)\right |.\]


Every other Monday (starting 01/22/24), we will post a problem to engage our mathematical community in the problem solving activity and to enjoy mathematics outside of the classroom. Students (both undergraduate and graduate) are particularly encouraged to participate as there is no better way to practice math than working on challenging problems. If you have a solution and want to be a part of it, e-mail your solution to Marcin Mazur ( by the due date. We will post our solutions as well as novel solutions from the participants and record the names of those who've got the most number of solutions throughout each semester.

When you submit your solutions, please provide a detailed reasoning rather than just an answer. Also, please include some short info about yourself for our records.

Previous Problems and Solutions

  • Problem 5 We did not receive any solutions.
  • Problem 4 A solution submitted by Beatrice Antoinette.
  • Problem 3 Solved by Mithun Padinhare Veettil.
  • Problem 2 A solution submitted by Sasha Aksenchuk.
  • Problem 1 Solutions submitted by Sasha Aksenchuk and Maximo Rodriguez.
pow/start.txt · Last modified: 2024/04/09 13:51 by mazur