Chirpy, There are no maths involved with your problem, whether you are cutting single cheek or double cheek hip rafters as your hips do not come into the equation at this stage, how ever you will have major problems on a double hip roof of this size.
Will write it up in laymans language that you should understand. Pitch would have been helpful but assume 35 degree with 50mm ridge board. Overall run = 11500, half run = 5750 less half of ridge = 5725 x a 35 degree secant of 1.221 = length of rafter = 6.984 from top plumb cut to heel of birdsmouth. First problem. To support that length of rafter you will need two rafters per slope with a wrap round purlin supported of either spline walls or treble joists.
Back to your problem. Two choices Ridge board all as your post 125mm long, set central to length of building and supported with pair of queens at each end,. Half thickness of ridge, ply collecting gusset at each junction end. This will then make your two kings at each end the same length as your two pairs of queens supporting ridge board.
Or increase length of ridge board by thickness of ridge board and this will make kings and queens same length.
Bear in mind if you are at 35 degree your rafters will be 35 seat and 55 plumb but your hips will be 26.5 seat and 63.5 plumb. You can work out hip length with a secant, but we always take a physical measure and drop the hip 12mm below HAP, be it single or double cheek.
Your other major problem is have you load bearing spline walls to support ceiling joists?
Fifty years ago we would have thrown this size roof up with out to much thought, but these days we would truss it as it will work out so much cheaper.
Regards oldun