I really don't know where to post this. GPL License question

[Spenceee]

I am a commercial software developer, and we are all for GPL code
etc.  However we have proprietary code and all the rest.

MY question in a nutshell is this:

My interpretation of the GPL is that if we were to use a GNU public
license piece of software in our application (Sumatra PDF reader is
the software in question) then we would be required to distribute ALL
the source code for our software?   Is my interpretation correct?

What we would like to do is leverage the software in some way, and
happily provide source code etc and any mods that we make to the GPL'd
software, but not provide source to the commercial software.

Is this possible or no?  Also feel free to burn me if this is the
wrong forum for this question, but please be constructive and tell me
the right forum...