Math Blues

I was gonna do a blog entry yesterday - honestly! I had a really nice one planned for 9/11, urging America to stay focused and everything. The whole deal. But then, this happened:

In the adjoining figure, two circles of radii 8 and 6 are drawn with their
centers 12 units apart. At P, one of the points of
intersection, a line is drawn in such a way that the chords QP
and PR have equal length. Find the square of the length of QP.

Once again, I stayed up till eleven, this time working on this problem (for my online math class). I have five pages of diagrams and equations on my desk, but I still haven't figured anything out. Here's yesterday's schedule:

9 PM: Finish homework. Decide to work on this problem (class meets tomorrow - err - today).

9:30 PM: Got nothing done. Ask dad for help. We proceed to work on it together.

10:00 PM: Dad has other things to do. I tell him that I'm giving up, go and eat dessert, and then for some strange reason am drawn back into the room. Keep working on it.

10:30 PM: For lack of a better approach, start drawing huge copies of the diagram and measuring. Estimate the answer to be 138 (plus/minus 2).

And I still haven't figured it out. If you have any ideas, feel free to post! Bob - this one's for you ;)