Mathematics

Problem

a, b, c

and

d

are the position vector of the vertices of a cyclic quadrilateral

ABCD

, prove that

\frac{a \times b + b \times d + d \times a}{(b-a) \cdot (d-a)} + \frac{b \times c + c \times d + d \times b}{(b-c) \cdot (d-c)} = 0