Question

a circle p is circumscribed about a regular hexagon abcdef
arcs ab, bc, cd, de, ef, fa are all equal
select one:
a. true
b. false

a circle p is circumscribed about a regular hexagon abcdef
if segment ad is drawn, adef is a
select one:
a. trapezoid
b. rhombus
c. rectangle
d. square

Explanation:

Step1: Analyze regular hexagon arcs

A regular hexagon has all sides equal. For a circumscribed circle, equal chords subtend equal arcs. Since $AB=BC=CD=DE=EF=FA$, their corresponding arcs are equal.

Step2: Analyze quadrilateral ADEF

In a regular hexagon, $AD$ is a diameter of the circumscribed circle, so $\angle AED$ and $\angle AFD$ are right angles (inscribed angles subtended by a diameter). Also, $AF \parallel DE$ (opposite sides of a regular hexagon segment are parallel), and $AD$ is not equal to $AF$. A quadrilateral with one pair of parallel sides and right angles is a rectangle.

Answer:

1. a. True
2. c. rectangle