MathDB
Distance constant

Source: APMO 1996

March 12, 2006
geometryperimeterratiorhombustrigonometryinvariantsymmetry

Problem Statement

Let ABCDABCD be a quadrilateral AB=BC=CD=DAAB = BC = CD = DA. Let MNMN and PQPQ be two segments perpendicular to the diagonal BDBD and such that the distance between them is d>BD2d > \frac{BD}{2}, with M∈ADM \in AD, N∈DCN \in DC, P∈ABP \in AB, and Q∈BCQ \in BC. Show that the perimeter of hexagon AMNCQPAMNCQP does not depend on the position of MNMN and PQPQ so long as the distance between them remains constant.
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