Question

If a circle is inscribed in a hexagon which of the following must be true. check all that apply.

A. The circle is congruent to the hexagonn

B. the circle is tangent to each side of the hexagon

C. each vertex of the hexagon lies inside the circle

D. the hexagon is circumscribed about the circle

E.each vertex of the hexagon lies outside the circle

Answer 1

B, D, E

Explanation:

INscribed means "scribed", "scribbled", "drawn", ... inside another picture so that the edges and/or cornes of the inner object touch the edges and corners of the outer object.

it is the opposite of CIRCUMscribed.

a circle touching a line (not cutting through, just touching) means the line is a tangent.

"vertex" is the nice word for the corners of an object. but since the circle is only touching (at one point) each side of the hexagon, the corners of the hexagon m must be outside the circle.

under no circumstances can an object with corners (like a hexagon) be congruent with a smooth object without corners (like a circle). congruent means that they can cover each other completely up without any part lapping over or "leaking" through.

Answer 2

A. The circle is congruent to the hexagon

False. This is not always true since the size and the hexagon can be different sizes.

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

True. A tangent line is defined as a line that touches a curve at a point, but does not cross it at that point. The circle would touch each side of the hexagon, so the circle would be tangent to each of the hexagon's sides.

C. Each vertex of the hexagon lies inside the circle

False. The vertexes of the hexagon is where two of the sides intersect, which is just not possible to lie inside the circle since the circle is already inside the hexagon, not the other way around.

D. The hexagon is circumscribed about the circle

True. Since the circle is inscribed in a hexagon, the hexagon is circumscribed about the circle.

E. Each vertex of the hexagon lies outside the circle

True. This is the opposite of statement C.