Triangle defined by one point IV

Let points $A(a,0,0), B(0,b,0), C(0,0,c)$ be vertices of the triangle. Triangle sides are: $AB^2 = a^2+b^2, AC^2=a^2+c^2, BC^2=c^2+b^2$ Coordinates of the incentre are calculated using the system of 3 equations as follows: $a*BC/(AB+AC+BC)=979$ $b*AC/(AB+AC+BC)=2379$ $c*AB/(AB+AC+BC)=2500$ The equations solution is: $a=2332, b=6201,c=12720$ The perimeter can be calculated as $33708$