A rectangle hexagon is inscribed in a circle. Each of the 6 sides of the hexagon is 8 units in length. Find the radius of the circle. 8 4 6 16
A rectangle hexagon is a hexagon that can be divided into six rectangles. In this case, each rectangle has two sides that are parallel to the radius of the circle.
If we draw two radii from the center of the circle to opposite vertices of the rectangle hexagon, we can see that each radius is also the height of one of the rectangles.
The length of the rectangle is equal to the length of the hexagon's side, which is given as 8 units.
Since the rectangle is formed by two congruent triangles, we can use the Pythagorean theorem to find the length of the other side of the rectangle. Let's call this length "x".
Using the Pythagorean theorem, we have:
$$x^2 + \left(\frac{8}{2}\right)^2 = 8^2$$
Simplifying this equation, we get:
$$x^2 + 4^2 = 8^2$$
$$x^2 + 16 = 64$$
$$x^2 = 64 - 16$$
$$x^2 = 48$$
Taking the square root of both sides, we get:
$$x = \sqrt{48}$$
$$x = \sqrt{16 \cdot 3}$$
$$x = 4 \sqrt{3}$$
Therefore, the length of the other side of the rectangle is $4 \sqrt{3}$ units.
Since we know that the radius of the circle is equal to the height of the rectangle, the radius of the circle is $4 \sqrt{3}$ units.
Thus, the correct answer is $\boxed{4 \sqrt{3}}$ units.