MathDB

Let

ABCD

be a cyclic quadrilateral. Let

M, N

be the midpoints of the diagonals

AC

and

BD

and let

P

be the midpoint of

MN

. Let

A',B',C',D'

be the intersections of the rays

AP

BP

CP

and

DP

respectively with the circumcircle of the quadrilateral

ABCD

.
Find, with proof, the value of the sum

\sigma = \frac{ AP}{PA'} + \frac{BP}{PB'} + \frac{CP}{PC'} + \frac{DP}{PD'} .

7.2