find points that are within a circle given center and radius

Question

We have a point (x,y) and some other points (xi,yi). How can we determine wich of (xi,yi) points are within a circle with center (x,y) and radius d (a given number) Thanks

Answer 1

Simple way.

Compute the distance from the point to the center of the circle. If less than radius , then its within the circle.

Answer 2

If sqrt((xi-x)^2 + (yi-y)^2) <= d

Answer 3

(xi-x)**2 + (yi-y)**2 < r**2

Answer 4

If (xi - x)^2 + (yi - y)^2 is less than d^2, it's inside. If it equals d^2, it's on the circle. If it's greater than d^2, it's outside.