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X(4), X(76), X(98), X(511), X(1342), X(1343), X(5004), X(5005), X(9469), X(11610), X(15407), X(32618), X(32619) vertices of the cevian triangle of X(290) |
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Geometric properties : |
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K1134 = psK(X98, X290, X4) is the isogonal transform of K570 and also the antigonal image of K1131. K1134 is a circular cubic with singular focus X(12188). Note that the tangents at A, B, C to K1134 are the symmedians since the pseudo-isopivot is X(6). K570 and K1134 meet at A, B, C, X(98), X(511), the circular points at infinity, hence at two other finite points T1, T2. These points are isogonal conjugates and lie on the line passing through X(2) and X(51). It follows they must lie on the circum-conic passing through X(6), X(95), X(98), X(182), X(183), X(2980), etc, and obviously on the Thomson cubic K002. K1134 is the locus of pivots of circular pKs which pass through X(98). The locus of the isopivots is K1129. See K336, K653 for instance. |