There are several different (but equivalent) ways to define $\limsup$ and $\liminf$, so it all depends on which one you are familiar with.
One definition is that $\limsup x_k$ is the supremum of all points that are limits of subsequences of $x_k$. That is, $\limsup x_k = \mathrm{sup}\Bigl\{ a\in\mathbb{R}\cup\{\pm\infty\}\Bigm| \text{there is a subsequence of }x_k\text{ that converges to }a\Bigr\}$ (where we think of a subsequence as "converging to $\infty$" or "to $-\infty$" if the limits are equal to $\infty$ or $-\infty$). Similarly, one can define $\liminf x_k$ to be the infimum of all points that are limits of subsequences of $x_k$.
Note that a real number $a$ is a limit of a subsequence of $x_k$ if and only if $a$ is a cluster point for the sequence $x_k$. Given this, the fact that $c$ is a cluster point of $x_k$ tells you that $c$ belongs to that set for which $\limsup x_k$ is the supremum, and $\liminf x_k$ is the infimum. So what conclusion can you draw then?
If you have other definitions of $\limsup$ and $\liminf$, then please state the ones you know explicitly in your question.