[Geometry] Chords of circles

I had this problem in the 'Canadian open mathematics challenge', and I haven't the faintest Idea how to solve it. If anyone knows how to do this, I'd really appreciate it.


The two circles C1 and C2 have a common chord AB. Point P is chosen on C1 so that it is outside C2. Lines PA and PB are extended to cut C2 at X and Y, respectively. If AB=6, PA=5, PB=7 and AX=16, determine the length of XY.

I've been able to solve for BY, but beyond that I'm stumped. A diagram was provided, but I can't reproduce it in ASCII.

If I'm picturing this correctly (I drew what you're said), then there should be a nice little triangle there, PXY. There would also be a triangle PAB.

Triangle PAB is similar to PXY, meaning line segment AB is to line segment XY as line segment PX is to line sengment PA.

There are two triangles, but they aren't similar. I'll try to get a diagram put together.

draw it in paint and save it as a .jpg or something. That would work well.

Remember that the diagrams are not always drawn accurately. Sometimes they're drawn to confuse... (SAT does that, I believe)

I just drew up another diagram, and I must be missing something, because I still come up with 2 similar triangles, just not the ones I described. put up a diagram so I don't try to confuse you.

It's not a perfect diagram, but it gives enough information, and The triangles are definitely not similar, unless I'm missing something important here.

Well, I've been working on this and can't find the answer i just need the segment BY. And you say that you can find it, tell me how to find BY and then I can find XY.