1. Polygons: Inscribed and Circumscribed
Lesson 3.5
Polygons: Inscribed and Circumscribed pp

2. Objectives:
1. To identify inscribed and circumscribed polygons.
2. To define an inscribed angle of a circle.
3. To identify tangents and related terms.

3. Definition
An inscribed polygon is a polygon whose vertices are points of a circle.

4. A B C D E
Inscribed pentagon

5. Definition
An inscribed angle is an angle whose vertex is on a circle and whose sides each contain another point of the circle.

6. A B C A B E C D
Inscribed angle: ABC

7. When a polygon is inscribed in a circle, the circle is circumscribed about the polygon.Q L

8. Definition
A polygon circumscribed about a circle is a polygon whose sides each intersect the circle in exactly one point.

9. Circumscribed triangleP•
Circumscribed triangle

10. Definition
A tangent line (or tangent) is a line in the plane of a circle that intersects the circle in exactly one point.
The point of tangency is the point at which a tangent line and a circle intersect.

11. Definition
A tangent segment is a segment of a tangent line that contains the point of tangency.

12. A B C Y X P• Z

13. Practice: Determine whether the polygon is (1) inscribed, (2) circumscribed, or (3) neither.

14. Practice: Determine whether the polygon is (1) inscribed, (2) circumscribed, or (3) neither.

15. Practice: Determine whether the polygon is (1) inscribed, (2) circumscribed, or (3) neither.

16. Homework pp

17. ►A. Exercises
Look at the diagram in exercises 1-5 and state whether the polygons are circumscribed about a circle, inscribed in a circle, or neither. 1.

18. ►A. Exercises
Look at the diagram in exercises 1-5 and state whether the polygons are circumscribed about a circle, inscribed in a circle, or neither. 5.

19. ►A. Exercises 7. Is polygon ABCDE inscribed in circle S?
Use the figure for exercises 6-10.
7. Is polygon ABCDE
inscribed in
circle S? S A E D C B M N O P L

20. ►A. Exercises 11. Name three points on circle L.
Use the figure for exercises
11. Name three points on
circle L. L O N M

21. 13. Is MO tangent to circle L? Why?
►A. Exercises
Use the figure for exercises
13. Is MO tangent to circle L?
Why? L O N M

22. ■ Cumulative Review
True/False. Correct any incorrect statements and justify correct statements with a definition, theorem, or postulate.
22. If AB  BC, then AB = BC.

23. ■ Cumulative Review
True/False. Correct any incorrect statements and justify correct statements with a definition, theorem, or postulate.
23. If AB  BC, then AB = BC.

24. ■ Cumulative Review
True/False. Correct any incorrect statements and justify correct statements with a definition, theorem, or postulate.
24. If AB = BC, then B is the midpoint of
AC.

25. ■ Cumulative Review
True/False. Correct any incorrect statements and justify correct statements with a definition, theorem, or postulate.
25. If AB  BC, then A = C.

26. ■ Cumulative Review
True/False. Correct any incorrect statements and justify correct statements with a definition, theorem, or postulate.
26. If B is the midpoint of AC, then AB 
BC.