Circle Geometry


This page offers formal proofs for the derivation of circles tangential to other graphic elements, and implementation of those proofs in the C# language.


We make this work available as a public service as it is often difficult to find advanced geometric proofs.


You may use the code freely for your personal use or for educational purposes.  You may also use the code in commercial programs at no charge, provided that acknowledgement is made to Arc en Ciel Ltd in the About box, or in the documentation.


We invite comments or suggestions. Please click here to send us an email.




C# code

Circle passing through three points



Circles tangential to three lines



Circles tangential to two lines and a circle



Circles tangential to a line and two circles



Circles tangential to three circles




Other constructions may be conveniently derived from the above.  For example, a circle passing through a point and tangential to a line and to another circle may be derived by using the code for a circle tangential to a line and two circles, and putting the radius of one of the circles to zero.

See for further analysis and references. 






Arc en Ciel Ltd was founded in 1989 and specialised in CAD/CAM applications. The documents above are derived from work done during that period.


The company focus shifted to the GIS field and Arc en Ciel now specialises in addressing and mapping solutions for the UK.  UK users that might be interested in our products are invited to click here.