It presents a vivid and highly stimulating path from the Apollonius circles through conic sections to harmonic reflection. In the Apollonius circles, Euclidean and projective geometry meet and connect. As a geometric locus of all points with a constant distance ratio to two fixed points, the two foci, they can be viewed in the sense of Euclidean geometry. This leads to the harmonic position of the internal and external division points in relation to the foci. The entirety of all Apollonius circles allows for a clear experience of the harmonic involution of the division points. Harmonic position and harmonic involution are also fundamental concepts in projective geometry. These and other connections lead to the surprising discovery by Astrid Baumann that ellipses, parabolas, and hyperbolas can be generated as envelopes of Apollonius circles.