- Let ABC be a triangle, IaIbIc the excentral triangle, P a point
and A'B'C' the cevian triangle of P.
Denote A* = B'Ic /\ C'Ib, B* = C'Ia /\ A'Ic, C* = A'Ib /\ B'Ia
Which is the locus of P such that
1. ABC, A*B*C*
2. A'B'C', A*B*C*
Let ABC be a triangle.
A line L passing through A intersects the circle with diameter AB again at Ab and the circle with diameter AC again at Ac.
[Equivalently: Let Ab, Ac be the orthogonal projections of B, C on L, resp.]
Let A* be the intersection of BAc and CAb.
Which is the locus of A* as L moves around A?
Parametric trilinear equation:
1/u(t) = a*((b^2+c^2-a^2)^2-4*b^2*c^2*c os(2*t)^2)/(2*S)
1/v(t) = 2*(cos(2*t)*c-b)*S - c*sin(2*t)*(a^2+3*b^2-2*cos(2* t)*b*c-c^2)
1/w(t) = 2*(cos(2*t)*b-c)*S + b*sin(2*t)*(a^2+3*c^2-2*cos(2* t)*b*c-b^2)