Can someone help me solve the following question please?

Let v be a vertex of a d-polytope P such that $\displaystyle 0 \in intP $ .

Prove that $\displaystyle P^* \cap \{y \in \mathbb{R}^d \mid\left < y, v\right>=1\ \} $ is a facet of $\displaystyle P^{*} $.

The definitions are:

$\displaystyle P^*=\{ y\in\mathbb{R}^{d}\mid\left < x, y\right>\leq 1\ \forall x\in P\} $

and a face of P is the empty set, P itself, or an intersection of P with a supporting hyperplane (i.e.- a hyperplane, such that P is located in one of the halfspaces it determines).

A facet is a face of maximal degree

Thanks