hi alessandro,

if the distances from those 3 points to (-1,2) are equal,

then, as they are equidistant from that point,

then (-1,2) can be used as the centre of a circle for which the radius

is the distance from (-1,2) to those 3 points.

Hence, to prove, you can use the distance formula

to calculate the distance from (-1,2) to the 3 points.

This is Pythagoras' theorem in co-ordinate form.

If the distances are the same, the 3 points lie on the circle circumference.