How this calculation works
Find the distance between tangency points along external and internal common tangents.
External: √(d²−(r₁−r₂)²), internal: √(d²−(r₁+r₂)²)A worked example
Radii 5 and 2 at distance 10 give external length √91 and internal length √51.
Good to know
A negative radicand means the corresponding tangent does not exist.
Reference: OpenStax Algebra and Trigonometry, Trigonometric Applications (opens in a new tab) ↗
Read the result
Find the distance between tangency points along external and internal common tangents.
The primary result is labeled “External tangent segment”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A negative radicand means the corresponding tangent does not exist.
For a related exercise, try the circle calculator.
A few questions, answered
How can I check the default inputs by hand?
Radii 5 and 2 at distance 10 give external length √91 and internal length √51.
Which rule does this calculator apply?
External: √(d²−(r₁−r₂)²), internal: √(d²−(r₁+r₂)²)