Helly's theorem is stated as:
Helly's theorem: Let $C_1, \cdots, C_n \subseteq \mathbb{R}^d$ be convex sets such that any $d+1$ of them intersects. Then all $C_i$ have a common point.
Nerve theorem is stated as:
Nerve theorem: If $U$ is a good cover ($U$ is a good cover if $U$ is a finite family of closed subsets on a topological space $X$, and every non-empty intersection of sets in $U$ is contractible to a single point), then $|N(U)|$ is homotopy equivalent to $\bigcup U$, where $N(U)$ is the nerve of $U$ and $|\cdot|$ is the underlying topological space of nerve.
I learned Helly's theorem in geometry class, and recently lecturer of topology told us we can use Nerve theorem to prove Helly's theorem, but these two theorems seem to be in completely different field, how can we prove Helly's theorem using Nerve theorem? Or any hints, intuition, etc..
Thanks in advance.