\[L = \sqrt{d^2-(r_1+r_2)^2}\]
Variables
Lcommon internal tangent length
ddistance between centers
r1radius of first circle
r2radius of second circle
Description
What is this formula?
This formula calculates the length of the common internal tangent between two circles. The tangent crosses the region between the circle centers while touching both circles.
When to use it
Use this formula when the radii of two circles and the distance between their centers are known and the internal tangent length needs to be determined.
Example
If the distance between centers is 13 m, with radii 3 m and 4 m:
L = √(13² - (3+4)²) = 10.954 m
Applications
- Geometry and trigonometry
- Mechanical engineering
- Pulley and belt systems
- CAD and technical drawing
- Machine and mechanism design