$A = (0,0),B = (4,0),C = (1,2)$
How can I find the barycentric coordinates of the orthocenter of $\triangle ABC$?
2026-04-25 19:08:30.1777144110
how to find the barycentric coordinates of the orthocenter
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This Wikipedia page describes the orthocentre in barycentric coordinates of the triangle $ABC$ as $$ \left((a^2+b^2-c^2)(a^2-b^2+c^2):(a^2+b^2-c^2)(-a^2+b^2+c^2):(a^2-b^2+c^2)(-a^2+b^2+c^2)\right), $$ where $a=|BC|,b=|CA|$ and $c=|AB|$ are the side lengths of the triangle.