Two circles  $C_1$  and  $C_2$  of radii 8 each are placed inside a semicircle C of radius 25. The 
two circles $C_1$  and  $C_2$  are each tangent to the diameter of semicircle C and also tangent  to the semicircle C. The length of direct common tangent of  $C_1$  and  $C_2$ is  a, The length  of transverse common tangent of $C_1$  and  $C_2$ is b and The inradius of triangle formed by  joining centers of circles $C,C_1,C_2$  is c. Then the value of  $a+b^2+c$  is ___