Distance between Orthocenter and Center of Taylor Circle

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Given a triangle , let , , be the feet of the perpendiculars to the sides opposite , , . (These perpendiculars are the altitudes, drawn dashed red; they intersect at the orthocenter .) Draw two perpendiculars each from , , to the sides of to get six green points. These six points are concyclic, defining the Taylor circle with Kimberling center [1].


Let , , be the side lengths of , let be the circumradius of and let be the Brocard angle of .







You can drag the vertices , and .


Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA




[1] C. Kimberling. "Encyclopedia of Triangle Centers." (Aug 2, 2022) faculty.evansville.edu/ck6/encyclopedia.

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