One chord and two segments

Three segments, [AB] of length $a$, [BC] of length $b$ and [CD] of length $c$ are perpendicular to each other.


The circle passing by the points A,B,D has a radius $r$

How many triples $(a,b,c)$ such as $1\le a,b,c\le 1000$ and $GCD(a,b,c)=1$ are there such as $r$ is an integer?

Answer format: $count,\sum a,\sum b,\sum c$

You are given: $4,30,18,10$ for a threshold of $10$