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--- pow:problem1f25 [2025/09/09 05:20] – created mazur
+++ pow:problem1f25 [2025/09/12 13:34] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange|  Problem 1 (due Monday, September 8 )>
+A point $P$ inside a convex quadrilateral $ABCD$ is such that the triangles $ABP$, $BCP$, $CDP$, $ADP$
+have all the same area. Prove that one of the diagonals halves the area of the quadrilateral.
+</box>
+We received solutions from Raisha Chowdhury, Gerald Marchesi, Josiah Moltz, and Mathew Wolak.
+The solution submitted by Gerald Marchesi is particularly simple assuming familiarity with the concept
+of cross product of vectors in $\mathbb R^3$. For details and other solutions see the following link {{:pow:2025fproblem1.pdf|Solution}}.