Reflections of AH,BH,CH

Let ABC be a triangle.

Denote:

La, Lb, Lc := the reflections of AH,BH,CH in AI,BI,CI, resp.

Lab, Lac := the reflections of La in BH, CH, resp.

A* := Lab /\ Lac

Similarly B*, C*

The Triangles ABC, A*B*C* are perspective.

Perspector ?

Generalization:

P,P' instead of H,I
Special Case: P,P' = isogonal conjugate points.

APH, 17 December 2011

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For H and I, the perspector is X68.

For P and P' = isogonal conjugate of P, for P = H and P' =(u:v:w) and for P=(u:v:w) and P'=I the loci equations are long.

Since it is true for P = H and P' = I, it would be convenient to think in a function f such that f(H)=I and consider P and P'=f(P)

Francisco Javier García Capitán
18 December 2011