Sentence:  It follows that "O" lies on the circle of Apollonius for "A" and "C" and ratio "OT"/"OC", and on the <WSD>circle of Apollonius</WSD> for "B" and "C" and ratio "OT"/"OC". Point "O" is thus found at the intersections, if any exist, of these two <WSD>circles of Apollonius</WSD>. The details are left to the reader. 
Meaning of the word marked with <WSD> tags:  (geometry) The figure (a generalised circle) definable as the locus of points "P" such that, for given points "A", "B" and "C", <small>\frac{|AP|}{|BP|} = \frac{|AC|}{|BC|}</small>.