Geometry: butterfly porism


Butterfly Porism:  Given a circle and a line and four points on the line.  If there exists a quadrilateral inscribed in the circle through the four points then there exists an infinitely many such quadrilaterals.

Move the red point on the circle to see that the fourth point (blue) does not move! 
You may also move the yellow points to change the position of the line.
Move the red points on the line to change the butterfly's setup.

See the Butterfly in motion.
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