Bruce Shawyer, Some Remarkable Concurrences,

Forum Geometricorum, 1 (2001) 69 -- 74.

Abstract:   In May 1999, Steve Sigur, a high school teacher in Atlanta, Georgia, posted on The Math Forum, a notice stating that one of his students (Josh Klehr) noticed that

Given a triangle with mid-point of each side. Through each mid-point, draw a line whose slope is the reciprocal to the slope of the side through that mid-point. These lines concur.

Sigur then stated that ``we have proved this''. Here, we extend this result to the case where the slope of the line through the mid-point is a constant times the reciprocal of the slope of the side.

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