Intersecting chords

In a circle, two perpendicular chords AB and CD intersect in P.

We have the following lengths:
- $\parallel AP\parallel =a$
- $\parallel PB\parallel =b$
- $\parallel CP\parallel =c$
- $\parallel PD\parallel =d$
and $a<b,c<d\mathrm{\&}a<c$

Given that $a,b,c,d\text{ are positive integers }\le 5000$, how many distinct circles (distinct radius) can we found?

You are given: 1913 // For a threshold of 100

My timing: 60 sec