MathDB
Perpendicular diagonals

Source: Dutch Mathematical Olympiad 1998

October 29, 2005
geometryrhombusvector

Problem Statement

Let ABCDABCD be a convex quadrilateral such that AC⊥BDAC \perp BD. (a) Prove that AB2+CD2=BC2+DA2AB^2 + CD^2 = BC^2 + DA^2. (b) Let PQRSPQRS be a convex quadrilateral such that PQ=ABPQ = AB, QR=BCQR = BC, RS=CDRS = CD and SP=DASP = DA. Prove that PR⊥QSPR \perp QS.
Back to ProblemsView on AoPS