The Spieker center is the center Sp of the Spieker circle, i.e., the incenter of the medial triangle of a reference triangle Δ A B C. It is also the center of the excircles radical circle. It has equivalent triangle center functions α_10 | = | b c(b + c) α_10 | = | (b + c)/a, and is Kimberling center X_10. The Spieker center is also the centroid of the perimeter of the original triangle, as well as the cleavance center (Honsberger 1995; illustrated above).
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