Recent content by lolerlol

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    Proving a Convex Quadrilateral is a Square with Internal Point O as its Center

    Homework Statement Let O be an internal point of a convex quaddrilateral PQRS whose area is A. Prove that, if 2A = OP^2 + OQ^2 + OR^2 + OS^2, then PQRS is a square with O as its centre Homework Equations The Attempt at a Solution I have no idea where to start, except that I...
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    Proving the Cyclic Quadrilaterals in Altitudes Problem | Geometry Help

    Homework Statement Let AD be and altitude of triangle ABC where angle A is 90 degrees. Squares BCX1X2, CAY1Y2 and ABZ1Z2 are drawn outwards from the sides. Let AX1 meet BY2 in U and AAX2 meet CZ1 in V Prove that each of the quadrilaterals ABDU, ACDV and BX1UV is cyclic Homework...
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    Solve Squares & Numbers Homework: Diff > 5

    I don't quite understand. Could you explain further?
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    Solve Squares & Numbers Homework: Diff > 5

    Homework Statement A square is divided into 81 smaller squares by lines parallel to its sides. The numbers 1, 2, ..., 81 are entered in an arbitrary fashion, one in each square. Show that, however the numbers are entered, it is possible to find two small squares with an edge in common whose...
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