Find Direct Common Tangent of 2 Circles without Complexity

[Dumbledore211]

Homework Statement

Is there any direct formula for calculating the direct common tangent of two circles without having to go all the trouble of using y-y1=m(x1-x2) to derive it for two separate tangents t1 and t2. If there is could anyone explain to me how it is derived?

Homework Equations

The Attempt at a Solution

 

[ehild]

How would you draw those common tangents?

The problem can be reduced to the problem of drawing tangent from a point. Shrink (or blow up) the radius of the bigger circle by the radius of the smaller one. The tangent to the new circle from the centre of the smaller circle e is parallel to tangent line t.
It is easy to get angle theta from the distance of the centres (d) and the difference of the radii. Write up the equation of the green lines. They intersect the tangent points on the circles.

ehild