Droz_Farny

Droz Farny theorem

The sides of a triangle t = (FCG) are cut by two orthogonal lines a = (IL) and b = (OL) through the orthocenter of the triangle. Let M, P, N the cut-points of a with the sides of the triangle. Let R, Q, S be the corresponding cut-points with the sides of the other line b. Divide the segments MR, PQ and NS in fixed ratio k = DE/AB. through corresponding points U, T and V. Then these three points are on a line.
The blue curve is the envelope of the Droz-Farny lines, as the pivot point I varies on the circumcircle of t.

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