MathDB

4

Part of 1998 Dutch Mathematical Olympiad

Problems(1)

Perpendicular diagonals

Source: Dutch Mathematical Olympiad 1998

10/29/2005
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.
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