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Jacobi point
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The Jacobi point of an arbitrary triangle is a special point apparently discovered by Carl Friedrich Andreas Jacobi. It is found as follows. The points P, Q, and R are found such that ∠RAB ∠QAC, ∠PBC ∠RBA, and ∠QCA = ∠PCB. By Jacobi's theorem, the lines AP, BQ, and CR are concurrent, at a point K called the Jacobi point. The Jacobi point is a generalization of the Napoleon points. If the three angles above are equal, then K lies on the rectangular hyperbola given in areal coordinates by :<math>yz(\cot B - \cot C) + zx(\cot C - \cot A) + xy(\cot A - \cot B) = 0,</math> which is Kiepert's hyperbola. |
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