Basic Parameters of the Spieker Center
The Spieker center of a triangle is the incenter of the medial triangle of . It is also the center of the excircles's radical circle.[more]
Let , , be the exact trilinear coordinates of with respect to and , let , , be the side lengths opposite the corresponding vertices and let , , be the circumradius, inradius and semiperimeter of .
, , are the midpoints of , , , respectively.
is the pedal triangle of .
You can drag the vertices , and .[less]
A triangle center is said to be even when its barycentric coordinates can be expressed as a function of three variables , , that all occur with even exponents. If the center of a triangle has constant barycentric coordinates, it is called a neutral center (the centroid is the only neutral center). A triangle center is said to be odd if it is neither even nor neutral.
Standard barycentric coordinates of a point with respect to a reference triangle are normalized to have a sum of 1.
 C. Kimberling. "Encyclopedia of Triangle Centers." (Aug 9, 2022) faculty.evansville.edu/ck6/encyclopedia.