Math

Tangent of a Circle Calculator

Find the tangent length from an external point to a circle.

Calculated Output

Tangent length 12

Formula: tangent = √(d² − r²)

Step-by-Step Breakdown

1. Values used:

2. Circle radius = 5

3. Distance to centre = 13

5. Tangent length = 12

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The math behind it

The radius to the point of tangency is perpendicular to the tangent, forming a right triangle: tangent = √(d² − r²).

Radius 5, distance 13 → tangent √(169 − 25) = 12.

What if the point is inside the circle?

No tangent exists — the distance must be at least the radius.