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

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

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

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