Question

If acircle is inscribed in a hexagon, which of the following must be true ? Check all that apply.

A. The hexagon is circumscribed about the circle.
B. Each vertex of the hexagon lies inside the circle.
C. The circle is congruent to the hexagon.
D. Each vertex of the hexagon lies outside the circle.
E. The circle is tangent to each side of the hexagon.

Answer 1

A. The hexagon is circumscribed about the circle .
D. Each vertex of the hexagon lies outside the circle .
E. The circle is tangent to each side of the hexagon .

Answer 2

Answer: A. The hexagon is circumscribed about the circle.

D. Each vertex of the hexagon lies outside the circle.

E. The circle is tangent to each side of the hexagon.

Explanation:

Given: A circle is inscribed in a hexagon.

Then the hexagon is circumscribed about the circle.

Each vertex of hexagon lies outside the circle.

As each side of hexagon is just attached to the circle not passing through the circle, thus the circle is tangent to each side of the hexagon.

Since circle is a closed curve and hexagon is regular polygon with 6 sides, they cannot be congruent because they have different shapes.