If A(2, c) and B(d, 2) are two points such that the polar of one point with respect to the circle $x^2+y^2=16$, passes through the other, then c + d 

Given that A(2, c) and B(d, 2) are two points such that the polar of one point with respect to the circle $x^2+y^2=16$ passes through other

Here the points $A,B$ are conjugate points, the condition is $S_{12}=0$

it implies that 

$2c+2d=16\Rightarrow c+d=\boxed{\mathbf{8}}$