Editing Tangent (section)

==Tangent circles==
{{Main|Tangent circles}}

[[File:Tangent circles.svg|thumb|200px|Two pairs of tangent circles. Above internally and below externally tangent]]
Two distinct circles lying in the same plane are said to be ''tangent'' to each other if they meet at exactly one point.

If points in the plane are described using [[Cartesian coordinates]], then two [[circles]], with [[radii]] <math>r_1, r_2</math> and centers <math>(x_1, y_1)</math> and <math>(x_2, y_2)</math> are tangent to each other whenever

:<math>\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2=\left(r_1\pm r_2\right)^2.</math>

The two circles are called ''externally tangent'' if the [[Distance#Geometry|distance]] between their centres is equal to the sum of their radii,

:<math>\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2=\left(r_1 + r_2\right)^2.</math>

or ''internally tangent'' if the distance between their centres is equal to the difference between their radii:<ref>{{cite web| url = http://homepage.eircom.net/~phabfys/circles.html| title = Circles For Leaving Certificate Honours Mathematics by Thomas O'Sullivan 1997}}</ref>

:<math>\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2=\left(r_1 - r_2\right)^2.</math>