Question 859346
Let P & Q be the centers of the two circles

let MN be the tangent to both circles

Draw PM & QM the radii parallel to each other

From Q draw a parallel to MN to touch PM at T

So PTQ is a right triangle

angle PTQ = 90 

PQ is the hypotenuse
which is 25 units
PT = 11-4 = 7 units

Using Pytahgoras theorem
25^-7^2= QT^2

576=QT^2

QT=24

But QT = MN

there fore MN = 24 units

Draw the figure you will walk through