Apollonius by Adolfo Rodriguez is an Interactive Geometry Software (IGS, or Dynamic Geometry Environment, DGE) for the 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.
Video: the first construction is a regular hexagon given its center and one vertex. The second construction is the nine-point circle.
Click the figure below to see the video.
See more:
Interactive Geometry iPhone App