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Four Simson lines intersect; prove it's a rectangle

Source: 2012 Indonesia Round 2.5 TST 3 Problem 3

May 21, 2012
geometryrectanglegeometry unsolved

Problem Statement

Suppose l(M,XYZ)l(M, XYZ) is a Simson line of the triangle XYZXYZ that passes through MM.
Suppose ABCDEFABCDEF is a cyclic hexagon such that l(A,BDF),l(B,ACE),l(D,ABF),l(E,ABC)l(A, BDF), l(B, ACE), l(D, ABF), l(E, ABC) intersect at a single point. Prove that CDEFCDEF is a rectangle.
Should the first sentence read: Suppose l(M,XYZ)l(M, XYZ) is a Simson line of the triangle XYZXYZ with respect to MM. ? Since it appears weird that a Simson line that passes a point is to be constructed. However, this is Unsolved after all, so I'm not sure.
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