AMC 12 2020b Problem 15

There are 10 people standing equally spaced around a circle. Each person knows exactly 3 of the other 9 people: the 2 people standing next to her or him, as well as the person directly across the circle. How many ways are there for the 10 people to split up into 5 pairs so that the members of each pair know each other?

$\textbf{(A) } 11 \textbf{(B) } 12 \textbf{(C) } 13 \textbf{(D) } 14 \textbf{(E) } 15$