MathNet 2021 — Part 09 Question 70

Question 70

A regular hexagon of side length $1$ is inscribed in a circle. Each minor arc of the circle determined by a side of the hexagon is reflected over that side. What is the area of the region bounded by these $6$ reflected arcs?

$\frac{5\sqrt{3}}2-\pi$
$3\sqrt{3}-\pi$
$4\sqrt{3}-\frac{3\pi}2$
$\pi-\frac{\sqrt{3}}2$
$\frac{\pi+\sqrt{3}}2$