How could I prove the coordinate of the center of a circle which goes through three points with rational coordinates is rational?
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What kind of proof are you looking for? What are your thoughts on how to approach this? – Andrew Chin Dec 22 '19 at 14:51
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1Welcome to Mathematics Stack Exchange. Note that 3 points determine a circle – J. W. Tanner Dec 22 '19 at 15:01
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There is a question Get the equation of a circle when given 3 points which asks how to find the equation of the circle through three points. The method involves finding the centre and then the radius. Since their method of finding the centre revolves around solving a linear equation in the coordinates of the points and your points' coordinates are rational, the centre's coordinates will, likewise be rational. (unless the points lie on a straight line)
I apologise if this is unclear.
Reuben
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