Exeter point

Discovered to lie on the Euler line at a computers-in-mathematics workshop at Phillips Exeter Academy in $1986$, the Exeter point is the center of perspective of the tangential triangle 

(formed by the tangents to the circumcircle at the vertices $A,B,C$) and the circummedial triangle (whose vertices are points of intersection of the medians with the circumcircle). 

Trilinears for the Exeter point are

$a(b^4+c^4-a^4):$

$b(c^4+a^4-b^4):$

$c(a^4+b^4-c^4)$.