Tangencies

…Section”), “On Determinate Section,” “Tangencies,” “Vergings” (or “Inclinations”), and “Plane Loci,” and provides valuable information on their contents in Book VII of his Collection.

…Apollonius (in a work called Tangencies, which no longer survives) found the circle tangent to three given circles, or tangent to any combination of three points, lines, and circles. (The three-circle tangency construction, one of the most extensively studied geometric problems, has attracted more than 100 different solutions in the…