Question No. 10.

Question

The radii of two circles are 5 cms and 2 cms. The length of
the direct common tangents to the circles is 1.5 times the
length of the transverse common tangents. The distance
between the centers of the circles in cms

Answer 1

a few seconds with google will provide several discussions of this problem. For example, see

https://www.askiitians.com/iit-jee-coordinate-geometry/common-tangents.aspx