Exeter Point

Define $A'$ to be the point (other than the Vertex $A$) where the Median through $A$ meets the Circumcircle of $ABC$, and define $B'$ and $C'$ similarly. Then the Exeter point is the Perspective Center of the Triangle $A'B'C'$ and the Tangential Triangle. It has Triangle Center Function

$$\alpha=a(b^4+c^4-a^4).$$

References

Kimberling, C. ``Central Points and Central Lines in the Plane of a Triangle.'' Math. Mag. 67, 163-187, 1994.

Kimberling, C. ``Exeter Point.'' http://cedar.evansville.edu/~ck6/tcenters/recent/exeter.html.

Kimberling, C. and Lossers, O. P. ``Problem 6557 and Solution.'' Amer. Math. Monthly 97, 535-537, 1990.