A circle has center (3, -2) and radius 5. Which point lies on the circle?

A point is on the circle if its distance from the center $(3,-2)$ is $5$, that is, $(x-3)^2+(y+2)^2=25$. For $(6,2)$: $3^2+4^2=9+16=25$, so choice F works. Choice G, $(6,-2)$, gives $9+0=9$. Choice H, $(3,5)$, gives $0+49=49$. Choice J, $(0,-2)$, gives $9+0=9$. Only choice F reaches $25$. Notice that the points in choices G and J are only $3$ units from the center, and the point in choice H is $7$ units away, so they are inside or outside the circle rather than on it.