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

Drag the blue point to A.
Drag the centre (the red point) to different positions at which the circle also passes through B.
What is the characteristic of these positions?

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?

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Education Infrastructure Division, Education Bureau, Government of Hong Kong SAR. Created with GeoGebra