[code]LocusEquation[a^2+b^2==c^2,C][/code] asks GeoGebra to show the possible set of points of [i]C[/i] such that [math]a^2+b^2=c^2[/math]. This is true if and only if the triangle is right at [i]C[/i]. And this is true if and only if [i]C[/i] lies on the circle with diameter [i]AB[/i].