In a triangle PQR, $\angle{R} = \frac{\pi}{2}$. If $\tan (\frac{P}{2})$ and $\tan (\frac{Q}{2})$ are the roots of $ax^2 + bx + c = 0, a \neq 0$, then :

Question

( A ) $b = c$
( B ) $b = a + c$
( C ) $a = b + c$
( D ) $c = a + b$