The circle discussed in this paper is named after "The Great Geometer of Antiquity", that is Apollonius of Perga (ca. 262-190 BCE). Among his many contributions to geometry is a book with the title "Plane Loci." This book included, among others, a problem about the locus of a point moving in a plane such that the ratio of its distances from two fixed points is a positive constant different from one. It turned out that the locus is a circle now known as "Circle of Apollonius". The proof of this result is based on the following theorems: (1) The angle bisectors of a triangle; (2) Thales' theorem of the angle inscribed in a semicircle; and (3) The proportion resulting from a line drawn parallel to a side of a triangle. In fact, the proof connects these theorems in a nice way, and provides a refreshing idea about circles. The students can use Circle of Apollonius to tackle interesting, sometimes challenging, problems. (Contains 8 figures.)