The distance, from the origin of the normal to the curve, $x = 2 \cos t + 2 t \sin t,\; y = 2\sin t - 2t \cos t$ at $ t = \frac{\pi}{4}$, is:

Question

( A ) $2 \sqrt{2}$
( B ) $\sqrt{2}$
( C ) $2$
( D ) $4$