Length of Common External Tangent
Length of Common External Tangent
\[L = \sqrt{d^2-(r_2-r_1)^2}\]
Variables
L = common external tangent length (m)
d = distance between centers (m)
r1 = radius of first circle (m)
r2 = radius of second circle (m)
Description
What is this formula?
This formula calculates the length of the common external tangent between two circles. The tangent touches both circles without crossing the line between their centers.
When to use it
Use this formula when the radii of two circles and the distance between their centers are known.
Example
If the distance between centers is 10 m, with radii 2 m and 4 m:
L = √(10² - (4-2)²) = 9.798 m
Applications
- Geometry and trigonometry
- Mechanical engineering
- Belt and pulley systems
- CAD and drafting
- Machine design
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