r964

Let P be a point, XYZ its cevian triangle, X',Y',Z'  the reflections of X, Y, Z in the sides of ABC. Then AX', BY', CZ' concur at a point Q if P belongs to the Jerabek hyperbola (figure 1) or if P is at the infinite (figure 2). In this case, Q belongs to the ninecircle. If P is the circumcenter, Q is the Prasolov point.


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