Drawing a Circle passes through the 3 Vertices of a Triangle

Drag the blue point to A.

Drag the centre (the red point) to different positions at which the circle also passes through B.

Observe the marks of these positions. What are their characteristic?

What is the charateristic of the positions of the centre at which the circle passes through A and C?

How to draw the circle which passes thorough A, B and C?

http://www.geogebratube.org/material/show/id/3958 (Download GeoGebra file)