Explanation:

Correct option 1: 2:3

Radius of the circles are 4 cm and 6 cm.
Now, 
If two triangles are similar then the ratio of the corresponding sides of the triangles are equal.
Solution
Let us draw two circles with centre O and centre M and radius 4 cm and 6 cm respectively.
And the transverse common tangent touches the circle with centre O at A and touches circle having centre M at B and the transverse tangent and line joining A and B meets at C.
So, AO = 4 cm and BM = 6 cm
Now, In Δ AOC and Δ BMC, We have:

Angle A = Angle B = 90°( tangent and radius at same point are perpendicular to each other)
 Angle AOC = Angle BMC (OA and MB are perpendicular to the same line AB. So, OA || MB, Thus, by alternate angle theorem Angle AOC - Angle BMC)
Hence, ΔAOC≈ ΔBMC

therefore, AO/BM = OC/MC=4/6=2/3

Hence, The Required ratio is 2: 3.