Planes and spheres in 3D space – distance from center to plane

MathematicsVectors & Coordinate GeometryAges 17–18

In a rotatable Oxyz coordinate system, the plane (P): Ax + By + Cz + D = 0 and a sphere with center I and radius R are drawn together with the normal vector n = (A; B; C) and the perpendicular segment IH. The simulation computes d(I, (P)) with the distance formula and compares it to R to show whether the plane cuts the sphere in a circle (drawing that intersection circle, radius r = √(R² − d²)), is tangent to it, or misses it entirely.