## Locus

Expand Messages
• Let ABC be a triangle and PaPbPc the pedal triangle of point P. Denote: A B C the triangle bounded by the radical axes:
Message 1 of 240 , Mar 3, 2013
Let ABC be a triangle and PaPbPc the pedal triangle of point P.

Denote:

A'B'C' the triangle bounded by the radical axes:
((circle_with_diameter_OA),(circle_with_diameter_PPa)),
((circle_with_diameter_OB),(circle_with_diameter_PPb)),
((circle_with_diameter_OC),(circle_with_diameter_PPc)).

Which is the locus of P such that ABC, A'B'C'
are perspective?

H is on the locus. Perspector?

APH
• [APH]: 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.
Message 240 of 240 , Feb 16

[APH]:

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)

Regards,