- Let ABC be a triangle and A'B'C' the cevian / pedal
triangle of a point P.
Ab, Ac:=The orthogonal projections of B',C' on PC',PB',
A":= B'C' /\ AbAc.
Similarly Bc,Ba, B" and Ca,Cb, C".
Which is the locus of P such that:
1. AbAc, BcBa, CaCb are concurrent
2. A",B",C" are collinear.
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)