Given a pizza, represented by the unit disk $D_1(0,0)=\{(x,y)\in\mathbb{R}^2\mid \|(x,y)\|\leqslant 1\}$, and given $N$ slices of $r$-pepperoni, represented by disks $D_r(a_i,b_i)=\{(x,y)\in\mathbb{R}^2\mid \|(x,y)-(a_i,b_i)\|\leqslant r\}$, for $i\in[1..N]$.

Assume that the $N$ slices are randomly distributed on the pizza and that:

- for each $i\in[1..N]$, $D_r(a_i,b_i)\subseteq D_1(0,0)$; and
- for each $i,j\in[1..N]$, if $i\neq j$ then $D_r(a_i,b_i)\cap D_r(a_j,b_j)=\emptyset$.

Suppose that the pizza is shared by $2$ people. Is it always possible to slice the pizza along a single straight line such that the two parts have the same area (same amount of pizza) and the same total area of pepperoni?

What about generalizations to $K$ people and cuts along line segments?