OK. Another diagram below.

This one shows a circle in the middle (B) and one on the left that crosses it (A) and one on the right that just touches it (C) .

The tangent to B where it crosses A cuts A again.

The tangent to B where it touches C is also a tangent for C.

General rule. When two circles touch they share a common tangent.

A tangent is always at right angles to the radius at the point where the tangent touches.

So back to the previous diagram:

ABC = 90. If you give a letter to a fourth point, you'll complete a square. So BC = r

And AD is perpendicular to the common tangent at D (haven't drawn this line) and DC is too.

So ADC is a straight line.

Bob