How this calculation works
At the tangency point the radius is perpendicular to the tangent, so the distance to the centre is the hypotenuse.
THE FORMULA
t = √[(d−r)(d+r)]A worked example
At distance 13 from the centre of a radius-5 circle, the tangent length is 12.
Good to know
The point must be on or outside the circle.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Calculate the length from an external point to either point of tangency.
The primary result is labeled “Tangent length”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The point must be on or outside the circle.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
At distance 13 from the centre of a radius-5 circle, the tangent length is 12.
Which rule does this calculator apply?
t = √[(d−r)(d+r)]