For a point outside the circle, the tangent length comes from a right triangle.

The distance d is from the circle’s center to the external point, and it must be larger than the radius.

Enter the circle radius and the distance from the center to an external point. The calculator rejects points that are on or inside the circle.

1. Enter the radius.
2. Enter the center-to-point distance.
3. Read the tangent length from the result card.

With radius 5 and distance 13, the tangent length is 12.

That is the classic 5-12-13 right triangle relation.

The tangent formula is only valid for an external point, so the calculator rejects d <= r instead of producing a square root of a negative number.

Blank and malformed inputs are rejected explicitly, which prevents accidental zero-length tangents from silent parsing.