Some Triangle Centers Associated with the Circles Tangent to the Excircles

Abstract. We study those tritangent circles of the excircles of a triangle which enclose exactly one excircle and touch the two others from the outside. It turns out that these three circles share exactly the Spieker point. Moreover we show that these circles give rise to some triangles which are in perspective with the base triangle. The respective perspectors turn out to be new polynomial triangle centers. 1