Lines and circles in the coordinate plane

MathematicsVectors & Coordinate GeometryAges 15–16

Line Δ: ax + by + c = 0 has normal vector n = (a; b) and direction vector u = (−b; a) drawn right on the figure; circle (C) has center I and radius R. Drag center I, the free point M, or the whole line: distances d(I, Δ) and d(M, Δ) are computed from |ax₀ + by₀ + c|/√(a² + b²), and the relative position of Δ and (C) (secant, tangent, or no intersection) along with any intersection points, the angle between Δ and Ox, and the angle between Δ and IM update instantly.