Orthopolar Lines for a Quadrilateral

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Four given points form the quadrilateral and its diagonals and . The lines are two-colored to give triangles , , , and .

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Drop gray perpendiculars from the vertices of to the blue line to obtain new points . The cyan perpendiculars to , to and to are concurrent at the cyan orthopole. The orthopoles of the four component triangles of the quadrilateral are collinear, forming the black orthopolar line. If this construction is repeated, the red orthopolar line of the black orthopolar line is parallel to the original line .

You can drag the vertices of and two locators on the green line to move it.

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Contributed by: Ed Pegg Jr (May 2018)
Open content licensed under CC BY-NC-SA


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