i have some trouble proving this vector question:

The points A,B,C,D have position vectors **a, b, c, d **with respect to the origin O. The position vector **m**, of M on AC such that xAM=yMC, where x+y=1.

Show that if A,B,C,D are points on a sphere, centered at O, and if AC meets BD at M, where x¹BM=y¹MD with x¹+y¹=1, then

xy|**a-c**|²=x¹y¹|**b-d**|²

(bolded letters are vectors)