Kimberling’s point X(24)

1. Perspector of Triangle ABC and Orthic Triangle of the Orthic Triangle. Denote $T_0$ obtuse or acute $\triangle ABC.$ Let $T_0$ be the base triangle, $T_1 = \triangle DEF$ be Orthic triangle of $T_0, T_2 = \triangle UVW$ be Orthic Triangle of the Orthic Triangle of $T_0$ . Let $O$ and $H$ be the circumcenter and orthocenter of $T_0.$ Then $\triangle T_1$ and $\triangle T_2$ are homothetic, the point $P,$ center of this homothety lies on Euler line $OH$ of $T_0,$ the ratio of the homothety is $k = \frac {\vec PH}{\vec OP}= 4 cosA cosB cosC.$

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Kimberling’s point X(24)