Determine whether a point lies inside, on, or outside a circle.
Compare the distance from the point to the circle's center with the radius. If d < r → inside, d = r → on, d > r → outside.
Distance to Center
d = √((x−h)² + (y−k)²)
The point satisfies the circle equation exactly — it lies on the circumference.
The same principle applies in 3D with d = √((x−h)²+(y−k)²+(z−l)²).