29. Castillon's Problem
Castillon's Problem:
Inscribe in a circle a triangle whose sides pass through three given points.
This is Problem #29 of Heinrich Dörrie's 100 Great Problems of Elementary Mathematics.
The following constructions and theorems are used:
The power of a circle at a point: http://www.geogebratube.org/material/show/id/28302
Chord from a point and angle: http://www.geogebratube.org/material/show/id/30756