Proposition: Given four concyclic points (lie on
the same circumference) A,B,C,D, if four circles through AB,
BC, CD, and AD are drawn, prove that the remaining four intersections points
A', B', C', and D' of successive circles are concyclic.
Apollonius by Adolfo Rodriguez is an Interactive Geometry Software (IGS, or Dynamic Geometry Environment, DGE) for the
iPad, iPhone and iPod Touch. It allows you to make geometric constructions (such as those made using a compass and straightedge/ruler) and move their parts smoothly using the device's touchscreen.