We prove the following Main Theorem: $ZF + AD + V = L(R) \Rightarrow DC$. As a corollary we have that $\operatorname{Con}(ZF + AD) \Rightarrow \operatorname{Con}(ZF + AD + DC)$. Combined with the result of Woodin that $\operatorname{Con}(ZF + AD) \Rightarrow \operatorname{Con}(ZF + AD + \neg AC^\omega)$ it follows that $DC$ (as well as $AC^\omega$) is independent relative to $ZF + AD$. It is finally shown (jointly with H. Woodin) that $ZF + AD + \neg DC_\mathbf{R}$, where $DC_\mathbb{R}$ is DC restricted to reals, implies the consistency of $ZF + AD + DC$, in fact implies $\mathbb{R}^{\tt\#}$ (i.e. the sharp of $L(\mathbf{R}))$ exists.