Find the tangent points from an external point to a circle, plus the tangent angle. Used for blending arcs, laying out cams and programming tangential entry moves.
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Request a Proposal →Finding the tangent point on a circle is common when programming fillets, blending arcs, and computing lead-in/lead-out moves. This calculator finds the point on a circle at a given angle -- the basis for all tangent computations.
A tangent lead-in approaches the part contour along a tangential arc, preventing dwell marks at the entry point. The lead-in arc centre must be positioned such that the arc is tangent to both the approach line and the part contour. This calculator gives the tangent point coordinates.
A tangent line touches a circle at exactly one point and is perpendicular to the radius at that point. An intersection line crosses the circle at two points (secant) or one point (tangent -- the limiting case). Tangent transitions are smooth; intersection transitions have a corner.
Two circles are tangent when the distance between their centres equals the sum (external tangency) or difference (internal tangency) of their radii. The tangent point lies on the line connecting the two centres. Use this calculator to verify the point coordinates.
Enter the circle radius and the angle to the tangent point (from the positive X-axis). The calculator gives the X, Y coordinates of the tangent point and the perpendicular direction. Use these coordinates to program tangential arc entry and exit moves.
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