Locus

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• 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 /
Message 1 of 240 , Feb 1, 2013
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*

are perspective?

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,