HYACINTHOS 22900

ORTHOLOGIC CENTER OF ORTHIC AND REFLECTION TRIANGLE

By Randy Hutson, Cesar Lozada, Peter Moses

Trilinears a*((S^2-SA^2)*(SW-R^2)+2*S^2*SA)/SA : :

Barys: a^2 (a^2+b^2-c^2) (a^2-b^2+c^2) (a^4-2 a^2 b^2+b^4-2 a^2 c^2-b^2 c^2+c^4) (a^4 b^2-2 a^2 b^4+b^6+a^4 c^2-2 a^2 b^2 c^2-b^4 c^2-2 a^2 c^4-b^2 c^4+c^6)::

 

On lines {{4,93},{6,24},{25,195},{49,143},{52,539},{70,6145},{113,5446},{155,3060},{403,3574},{648,1179},{1112,2914},{1209,1216},{1843,5965},{1986,3575}}.

Reflection of X(i) in X(j) for these {i,j}: {54,973},{1493,143},{2914,1112}.

3 X[1209] - 2 X[1216].

3 X[54] - 5 X[3567].

6 X[973] - 5 X[3567].

X(4)-ceva conjugate of X(1594).

X(4)-crosspoint of X(3518).

X(3)-crosssum of X(3519).

X(2216)-isoconjugate of X(3519).

Trilinear product X(1594) X(2964).

Barycentric product X(1594) X(1994).

X(79) Orthic triangle.

{{1,21},{7,79},...} of Tangential triangle.

This point is also the orthic isogonal conjugate of X(1594), and X(79) of orthic IF ABC is acute.

 

APH