Hi! I'm not sure where to post this problem, but I guess under "Geometry" will do for now, right?

Well anyway, I'm having a little problem with circle geometry. It's my first time solving problems like the one I'm about to explain (I do, however, know the basics). Right, here I go:

Question: In a circle with center O, two chords AC and BD intersect at P. Show that LAPB = 1/2 (LAOB + LCOD).

(The 'L' is the symbol for angle, it should be in italics)

So the two normal lines, AC and BD, intersect at P (which could be anywhere in the circle). The middle of the circle, O, is the black squiggle. The dotted lines are the 'extra/invisible' lines which also make up triangles. And now...I have no idea how to solve it.

Any help would be greatly appreciated!