Orthologic Triangles

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If and are such that the perpendiculars from the vertices of one to a corresponding side of the other are concurrent at a point , we say that the two triangles are orthologic. (Regard a side as extending infinitely in both directions.) Using the labeling shown, this means that the perpendiculars from to , from to , and from to are concurrent. In 1827, Steiner discovered that this relation is symmetric. That is, if the perpendiculars from to , from to , and from to are concurrent, then the perpendiculars from to , from to , and from to are also concurrent. Drag the red disks to move the points , , , and . There are also three sliders to modify the sides of .

Contributed by: Jaime Rangel-Mondragon (July 2014)
Open content licensed under CC BY-NC-SA


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Reference

[1] O. Bottema, Topics in Elementary Geometry, 2nd ed. (R. Erné, trans.), Springer, 2008.



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