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K745
K745

u^3 (u (u + v + w) + 2 v w) x^2 (y - z) = 0

with u:v:w = cosA/2:cosB/2:cosC/2

X(1), X(2), X(7), X(18884)

K745 is the locus of P whose cevian triangle is perspective with the Mid-arc triangle. See TCCT 6.14.

K745 is a pivotal cubic with isopivot X(1) hence the tangents at A, B, C are the internal bisectors of ABC.

It is a member of a pencil of pKs passing through X(1), X(2), X(7) with the same tangents since the isopivot is always X(1). Their poles and pivots lie on the circum-conics with perspectors X(513) and X(514) respectively. This pencil contains K034, K317, K363, K365.

The pole and pivot P of K745 are now X(18883), X(18884) respectively.