When the 2 sides are along the coordinate axes then it is evident that the triangle must be a right angled triangle coz a 90 degree is formed at origin.
Thus the 3rd side will serve as the hypotenuse.
Now the circumcenter of a right triangle must lie on the mid point of hypotenuse.
Mark it as (alpha,beta) or (h,k).
Now find the point of intersections of the given lines
ax+by+c=0 and lx+my+n=0.
Find the equation of 3rd line in terms of h and k->yu can use intercept form here.
Now put the intersection point values in place of x and y of the newly formed equation of 3rd line.
Proceed now...i think yu will reach the answer.