Question 1177022
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            The question in this post is about the length of the common  INTERIOR  tangent to two non-overlying circles.


            I don't know  (don't sure)  if  @Matlower have read the problem and the question,  at all,

            but she answered  OTHER  question about the length of the common  EXTERIOR  tangent to two cirles.



            So,  her answer/solution is  NOT  RELEVANT  to the problem.



            THEREFORE,  I came to give you the link  (the reference)  to the real source.




See the lesson 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/geometry/HOW-TO-construct-a-common-interior-tangent-line-to-two-circles.lesson>HOW TO construct a common interior tangent line to two circles</A>

in this site.


The problem 2 of this lesson contains the solution to your problem.


Learn it from there.