Notice that A and E both lie on the circle. Recall the definition of center and radius of a regular polygon.
Different Statement: Find the apothem of polygon ABCDE. Both Answers: 6.8 and 5.5
Practice makes perfect
We are given the circle shown below with a circumscribed pentagon.
Let's check each of the given statements one at a time.
Statement 1
Find the radius of ⊙F.
We are asked to find the radius of the circle centered at F. From the diagram, we can see that E lies on the circle, and since FE=6.8, we can say that the radius of the circle is 6.8.
Statement 2
Find the apothem of polygon ABCDE.
By definition, the apothem is the distance from the center to any side of the regular polygon. From the diagram, we can see that the apothem is FG=5.5
Statement 3
Find AF.
Since A lies on the circle, then AF equals the radius of the circle. From the diagram, we can see that the radius is 6.8, and so AF = 6.8.
Statement 4
Find the radius of the polygon ABCDE.
By definition, the radius of a regular polygon is the radius of its circumscribed circle. Thus, we are asked to find the radius of ⊙F which is equal to 6.8.
Conclusion
As we can see, Statements 1, 3, and 4 ask for the radius of the circle, which is 6.8. In contrast, Statement 2 asks for the apothem of the polygon, which is 5.5.
Different Statement: & #2
Both Answers: & 6.8 and 5.5
