K1300


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	X(4), X(132), X(242), X(243), X(468), X(1503), X(5095), X(6110), X(6111), X(14847), X(41499), X(51219), X(51220), X(52458), X(52460), X(52461), X(52462), X(52463), X(52464), X(52465), X(52466), X(52467), X(52468), X(52469), X(53138), X(53139), X(69656), X(69657) vertices of the orthic triangle
Geometric properties :

K1300 is a strophoid with node H and singular focus X(132). The nodal tangents are parallel to the asymptotes of the Kiepert hyperbola.

K1300 is :

• the orthoassociate of the Kiepert hyperbola, i.e. its inverse in the polar circle.

• the pedal curve with respect to H of the inscribed parabola (P) with focus X(112).

• the barycentric product of H and the complement of K185 = cK(#X2, X523).

• the H-Hirst inverse of the rectangular hyperbola with center X(107) passing through X(1), X(4), X(19), X(920), X(1075), X(1249), X(1712), X(1713), X(1714), X(1715), X(2588), X(2589), X(3068), X(3069), X(3183), X(3186), etc.

• the isogonal cK with root X(2501) with respect to the orthic triangle. When ABC is acute, this is K040 of the orthic triangle.

• the locus of foci of conics inscribed in the orthic triangle whose center lies on the line HK.

See the analogous strophoids K591, K955, K1436.