Consider all the triangles having:

• All their vertices on lattice pointsInteger coordinates.
• CircumcentreCentre of the circumscribed circle at the origin $O$.
• OrthocentrePoint where the three altitudes meet at the point $H(5,0)$.

There are nine such triangles having a perimeter $\le 50$.
Listed and shown in ascending order of their perimeter, they are:

$A(-4,3)$, $B(5,0)$, $C(4,-3)$ $A(4,3)$, $B(5,0)$, $C(-4,-3)$ $A(-3,4)$, $B(5,0)$, $C(3,-4)$ $A(3,4)$, $B(5,0)$, $C(-3,-4)$ $A(0,5)$, $B(5,0)$, $C(0,-5)$ $A(1,8)$, $B(8,-1)$, $C(-4,-7)$ $A(8,1)$, $B(1,-8)$, $C(-4,7)$ $A(2,9)$, $B(9,-2)$, $C(-6,-7)$ $A(9,2)$, $B(2,-9)$, $C(-6,7)$

The sum of their perimeters, rounded to four decimal places, is $291.0089$.

Find all such triangles with a perimeter $\le {10}^5$.
Enter as your answer the sum of their perimeters rounded to four decimal places.