Circles: 2 semicircles are tangent to one another, and share a tangent line...

[tiny7smom]

I need help in figuring this out. Any help would be greatly appreciated.

Thank you !!

 

[Harry_the_cat]

I need help in figuring this out. Any help would be greatly appreciated.

Thank you !!View attachment 7786

If PB=6 then PF=6 (another radius)

If BC=6 then NC = 3 and so ME=3

Also PM = 6+3 = 9.

Now look at triangles DEM and DFP - they are similar. (AAA) Also recall the fact the tangent meets the radius at 90 degrees.
Let DM = x and use ratio of sides of similar triangles to find x.

You can figure out the rest from there.

 

[tiny7smom]

You are awesome!! Thank you so much.