ArchimedesTwinCircles
Archimedes proved that the purple circle, tangent to the enclosing circle, the red circle and the perpendicular dividing line, is congruent to the green circle tangent to the enclosing circle, the blue circle and the dividing line.
The trace checkbox shows a tracing point I used to help figure out that the centers of the twin circle should be on parabolas. (If you turn the point on,
try to move it while keeping two of the distances equal.)
The parabolas checkbox shows the parabolas that intersect to find the centers of the twin circles. They were defined using GeoGebra's parabola
tool that has input of the focus and the directrix.
I first saw the theorem at the Futility Closet, http://www.futilitycloset.com/2014/03/20/archimedes-twin-circles/