Distances between Triangle Centers

Distance between the Incenter and the Centroid of a Triangle.
Formula in terms of the sides a,b,c.

Distances between the Feuerbach Point and Incenter, Centroid, Nine Point Center and Spieker Center. 

Geometry Problem 626
Triangle, Distance from the Incenter to an Excenter.

Euler's Theorem: Distance between the Incenter and the Circumcenter.
Problem 155.

Distance between the Circumcenter and the Excenter.
Problem 157.

Distances between the Circumcenter, Incenter, and the Excenters.
Problem 159.