Let A', B', C' be the altitude feet;
A”, B”, C” their reflections in a line r through the orthocenter H; A*,
B*, C* the isogonals of A”, B”, C” in ABC. The circles {A”BC}, {B”CA},
{C”AB} have a common point and the same happens with the circles{AB”C”},
{BC”A”}, {CA”B”} (figure 1). The circles {A*BC}, {B*CA}, {C*AB} have a
common point and the same happens with the circles {AB*C*}, {BC*A*}, {CA*B*}
(figure 2). When r is the Euler line, two concurrence points are in the
ninecircle and two in the circumcircle of ABC.
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