The normal to the curve represented parametrically by 

$x=a(\cos \theta +\theta \sin \theta )\text{ and }y=a(\sin \theta -\theta \cos \theta )$

at any point $\theta$,  is such that it

$\frac{dy}{dx}=\tan \theta$, so equation the equation of normal is

$y-a(\sin \theta -\theta \cos \theta )=-\cot \theta (x-a(\cos \theta +\theta$

$\sin \theta )$ which simplifies to  $x\cos \theta +y\sin \theta =a.$

The distance of the normal from origin is $\left|a\right|\text{. }$