- Dear Antreas,

Let ABC be a triangle, P = (u:v:w) with cevian triangle A'B'C' and Q=(x:y:z) with anticevian triangle QaQbQc.

Denote A* = B'Qc /\ C'Qb, B* = C'Qa /\ A'Qc, C* = A'Qb /\ B'Qa.

A*B*C* is perspective with

(1) ABC at ( x/(-x/u+y/v+z/w) : y/(x/u-y/v+z/w) : z/(x/u+y/v-z/w)),

(2) A'B'C' at Q,

(3) QaQbQc at (x^2/u : y^2/v: z^2/w).

Note: A'B'C' and QaQbQc are perspective at the cevian quotient

P/Q = ( x(-x/u+y/v+z/w) : y(x/u-y/v+z/w) : z(x/u+y/v-z/w)).

Best regards

Sincerely

Paul - [APH]:aphGeneralization: (O) = a fixed conic.Which is the locus of Qp as P moves on the circle?Let (O) be a fixed circle, Q a fixed point and P a point on the circle.Let Qp be the orthogonal projection of Q on the tangent to circle at P.[Telv Cohl]