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Tangent Length from External Point Calculator

Enter circle radius and center-to-point distance, with the point outside the circle.

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Tangent length from external point

The point must lie outside the circle (distance > radius). Use one length unit; tangent length uses that unit.

Tangent length (input length unit): —

A QUICK WALKTHROUGH

How to use this tool

  1. Enter a positive circle radius.
  2. Enter a greater center-to-point distance.
  3. Calculate tangent length.

Right-triangle formula

For radius r and external point distance d>r, tangent length t=√(d²−r²). The radius is perpendicular to the tangent at the contact point.

Ideal geometry

Assumes an ideal circle and an external point in the same plane. Local calculation only.

GOOD TO KNOW

Common questions

Can the point be on or inside the circle?

This calculator excludes d≤r; d=r is a zero-length degenerate case.