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Distance between two origins

Hello =)

Here's my problem:(attached)

Basically I have two circles set up. I have the location of the origin of the circle to the left.

I also have the location of P1 and P2, and also the rotation of those points from the origin of the first circle. The two circles must intersect such that they intersect at the given points. The angle of the red line is exactly half way between the angle of the two given points.

I can make the radius of the second circle (r) whatever it needs to be, but it will always be larger than the radius of the first circle (R).

I'm trying to discover d, or the origin of the circle to the right (which can be derived from d), so that I can draw an inwards arc between two points.

I've wracked my brain for hours over this, any help would be very much appreciated. =)