Cambridge IGCSE Additional Mathematics · Syllabus 0606 · Coordinate Geometry of the Circle
Tangent to a Circle
What is Tangent to a Circle?
A straight line that meets a circle at exactly one point, called the point of contact. Algebraically, substituting a tangent into the circle equation produces a quadratic with a repeated root, so its discriminant is zero, and the perpendicular distance from the centre of the circle to a tangent is exactly equal to the radius. Geometrically, the radius drawn to the point of contact is perpendicular to the tangent there, which means the tangent gradient is the negative reciprocal of the radius gradient whenever both are defined. That perpendicularity is the standard method for finding a tangent equation in Cambridge IGCSE Additional Mathematics 0606, where no use of calculus is expected for this outcome. From a point outside the circle exactly two tangents can be drawn, and they have equal lengths from that point to their respective points of contact.
This definition is part of the Coordinate Geometry of the Circle chapter in Cambridge IGCSE Additional Mathematics.