equal, so the tangent lines coincide. This is true, for example, for the curve y = x 2/3, for which both the left and right derivatives at x = 0 are infinite; both the left and right tangent lines have equation x = 0. Tangent line to a space curve Tangent circles Two circles of non-equal radius, both in the same plane, are said to be tangent to each other if they meet at only one point. Equivalently, two circles, with radii of ri and centers at (xi, yi), for i = 1, 2 are said to be tangent to each other if Two circles are externally tangent if the distance between their centres is equal to the sum of their radii. Two circles are internally tangent if the distance between their centres is equal to the difference between their radii. Tangent plane to a surface The tangent plane to a surface at a given point p is defined in an analogous way to the tangent line in the case of curves. It is the best approximation of the surface by a plane at p, and can be obtained as the limiting position of the planes passing through 3 distinct points on the surface close to p as these points converge to p. Higher-dimensional manifolds More generally, there is a k-dimensional tangent space at each point of a k-dimensional manifold in the n-dimensional Euclidean space. See also Newton's method Normal (geometry) Osculating circle Osculating curve Perpendicular Subtangent Supporting line Tangent cone Tangential angle Tangential component Tangent lines to circles Tangent vector Multiplicity (mathematics)#Behavior of a polynomial function near a multiple root Algebraic curve#Tangent at a point References Sources External links Tangent to a circle With interactive animation Tangent and first derivative — An interactive simulation Differential geometry Differential topology Analytic geometry Elementary geometry