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.