(a) State and prove the Theorema Egregium.

(b) Let $X$ be a minimal surface without boundary in $\mathbb{R}^{3}$ which is closed as a subset of $\mathbb{R}^{3}$, and assume that $X$ is not contained in a closed ball. Let $\Pi$ be a plane in $\mathbb{R}^{3}$ with the property that $D_{n} \rightarrow \infty$ as $n \rightarrow \infty$, where for $n=0,1, \ldots$,

$$D_{n}=\inf _{x \in X, d(x, 0) \geqslant n} d(x, \Pi)$$

Here $d(x, y)$ denotes the Euclidean distance between $x$ and $y$ and $d(x, \Pi)=\inf _{y \in \Pi} d(x, y)$. Assume moreover that $X$ contains no planar points. Show that $X$ intersects $\Pi$.