Question 874871
Did not do it yet, but here is a strategy using coordinate geometry.


Two circles centered at the origin.
Small, {{{x^2+y^2=16^2}}}
Large, {{{x^2+y^2=34^2}}}


The tangent chord is at y=16, positioned horizontally with slope zero.  Use this to get the x value for the points on the larger circle.  Distance from the left x value to the y x value is the length of the tangent chord.