Yes, this is pretty simple using ideas I've been using for years. Basically the 3 lines form a triangle between them. The triangle you want is similar to this one. It is not difficult to place a fixed-angle moving triangle on the 3 lines such that the moving triangle can be made to coincide with the triangle formed by the lines. Then the moving triangle can also be placed such that all its sides are normal to the 3 lines. To explain the complete details takes lots of words. If you are still interested, e-mail me and I'll write the details. Steve Gray ----- Original Message ----- From: "David Gale" <gale@math.berkeley.edu> To: <math-fun@mailman.xmission.com> Sent: Wednesday, March 09, 2005 12:07 PM Subject: [math-fun] ortho-polygon

For those of you who are geometrically inclined, have you ever seen anything like,

Problem. Given n lines a_1,a_2,. . ,a_n in the plane in general position, Construct a (actually, the) polygon with vertices A_1,A_2, . . ,A_n, where Vertex A_i lies on a_i, and Segment A_iA_(i+1) is perpendicular to a_(i+1) (mod n).

dg

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