Question

a circle p is circumscribed about a regular hexagon abcdef
if segment ae is drawn, triangle aef is a/n __________ triangle.
select one:
○ a. isosceles
○ b. scalene
○ c. equilateral
○ d. right

a circle p is circumscribed about a regular hexagon abcdef
<fab is a/n __________ angle.
select one:
○ a. interior
○ b. central
○ c. exterior
○ d. inscribed

Explanation:

Step1: Analyze regular hexagon properties

In a regular hexagon circumscribed by a circle, all sides are equal, and each internal angle is $120^\circ$. The arc between adjacent vertices is $\frac{360^\circ}{6}=60^\circ$.

Step2: Evaluate $\triangle AEF$

• $AF = EF$ (sides of regular hexagon), so $\triangle AEF$ has two equal sides.
• Arc $EF$ is $60^\circ$, arc $AF$ is $60^\circ$, arc $AE$ is $120^\circ$. The inscribed angles corresponding to these arcs confirm two equal base angles. Thus, it is isosceles.

Step3: Classify $\angle FAB$

$\angle FAB$ is formed by two sides of the hexagon at vertex $A$, lying inside the boundary of the hexagon. This fits the definition of an interior angle.

Answer:

1. a. isosceles
2. a. interior