The incentre of the triangle formed by the lines , $4x+3y+10=0$ ,$5x-12y+26=0$ ,$7x+24y-50=0$  is

$4x+3y+10=0$ --------(1)

 $5x-12y+26=0$  ---------(2)             

 $7x+24y-50=0$  ----------(3)              

perpendicular distance from origin to   Equation (1) is  $\frac{\left|c\right|}{\sqrt{a^2+b^2}}=\frac{10}{5}=2$

Similarly distance from origin to equation (2) and  (3)  is  2 

(0,0) is equi distance from all sides, Incentre is equi distance from all sides Incenter = (0,0) as it is radius