# Tangent to Two Circles

## Tangent to Two Circles

A line that is tangent to two given circles.

There are five possible situations :

(1) If the two circles are disjoint circles, then there are 2 external tangents ($$d_{1}$$ and $$d_{2}$$) and 2 internal tangents ($$d_{3}$$ and $$d_{4}$$) :

(2) If the two circles are externally tangent, then there are 2 external tangents ($$d_{1}$$ and $$d_{2}$$) and 1 internal tangent ($$d_{3}$$) :

(3) If the two circle intersect, then there are 2 external tangents ($$d_{1}$$ and $$d_{2}$$) :

(4) If the two circles are internally tangent, then there is 1 external tangent ($$d_{1}$$) :

(5) If one of the circles is inside the other circle, then there is no tangent to the two circles :

### Example

The line ABabove is tangent to the two circles $$O_{1}$$ and $$O_{2}$$ at points A and B, respectively.