2021 Pascal Problem 16

In the diagram, Paths 1, 2 and 3 are drawn on a grid.

Paths 1 and 3 consist entirely of straight line segments. Path 2 consists of straight line segments and a semi-circle. If the length of Path 1 is x, the length of Path 2 is y, and the length of Path 3 is z, which of the following is true?

\textbf{(A)}\ x < y\ \text{and}\ y < z\quad \textbf{(B)}\ x < z\ \text{and}\ z < y\quad \textbf{(C)}\ x = z\ \text{and}\ z < y\quad \textbf{(D)}\ z < x\ \text{and}\ x < y\quad \textbf{(E)}\ y < z\ \text{and}\ z = x

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Pascal contests here.