Warm Up Section 4.1 Draw and label each of the following:

1. Warm Up Section 4.1 Draw and label each of the following: 1. 2. 3. 4. 5. A point , N, in the exterior of KLP 6. A point, W, in the interior of KLP

2. Answers to Warm Up Section 4.1 C B 2. 3. 1. A H G D K N 4. W L P

3. Introduction to Circles Section 4.1 Standard: MM2G3 bd Essential Question: How do I describe and denote the special characteristics of a circle?

4. D C B A F E Definition:A circle is the set of all points in a plane at a given distance from a given point. A. A circle is named by its center. The circle shown below has center C so it is called circle C. This is symbolized by writing C.

5. D C B A F E B. Draw a line segment by connecting points C and D in the circle above. The segment you have drawn is called aradius.The plural of radius is radii. Name three other radii of the circle. Be sure to use the correct notation for a line segment: ______ , ______ , ______ Note: one endpoint of the radius is the center of the circle and the other endpoint is a point on the circle. Also, all radii of a circle are congruent. So, if AC = 2 cm, then CE = _____ cm.

6. D C B A F E C. Now, make another segment by connecting points A and E. The segment you have drawn is called a chord. Name five other chords of the circle. ______ , ______ , ______ , ______ , ______ Note: both endpoints of a chord are points on the circle. Chords of a circle do not necessarily have the same length.

7. D C B A F E D. If a chord passes through the center of a circle it is given a special name. It is called a diameter. Name the diameter picturedin C. _________ Now, draw that diameter. Note: a diameter is the longest chord of a circle. Its length is twice that of the radius. So, if AC = 2 cm, then AB = _____ cm.

8. D C B A F E E. Next, draw a line passing through points B and F. The line you have drawn is called atangent. A tangent lies in the plane of the circle and intersects the circle in only one point. The point of intersection is called the point of tangency. What is the point of tangency for ? ________

9. D C B A F E F. Now, draw the line passing through points A and F. This line is called a secant. Any line that contains a chord of a circle is called a secant.

10. Use the circle below to identify the following: • Name the circle ________ • Name all radii pictured. • _____________ • Name all of chords pictured. • __________ • Name a diameter. • ________ • Name a tangent. • ________ • Name a secant • ________ K X Y K Z W

11. The points located inside a circle are called interior points. The points located on the circle are points of the circle itself. The points located outside the circle are called exterior points. Draw four lines that are tangent to both of the circles below at the same time. These lines are called common tangents.

12. The two common tangents that pass between the two circles above are called internal common tangents. The other two tangents are called external common tangents.

13. Draw all the common tangents possible for the problems below. 1. 2. 3.

14. Parts of circles are called Arcs. If the part of the circle is less than half the circle it is called a minor arc. If the part of the circle is more than half the circle it is called a major arc. And if it is exactlyhalf the circle it is called a semicircle.

15. The circle below has center P. Draw a diameter on your circle. Label the endpoints of the diameter H and K. Put another point on your circle and label it T. There are two semicircles pictured in your drawing. One can be symbolized HK and the other HTK . K T P H

16. K T P Name two minor arcs(you only need two letters to name a minor arc because you always travel the shortest distance unless told otherwise.) _______ , _______ Name two major arcs(you must use three letters to name a major arc because you always travel the shortest distance unless told otherwise.) _______ , _______ H HT TK KHT HKT

17. The circle below has center M. Mark two points on your circle and label them R and S. Now draw the following rays: and Color the inside of RMS. Name the arc that is inside the colored part of the angle. This is called the intercepted arc. Arc: ________ The angle is called acentral anglebecause its vertex is the center of the circle. S R M RS

18. S R M Arcs are measured in degrees. The measure of the intercepted arc is equal to the measure of the central angle that forms that arc. So, if mRMS = 60o, then m RS = 60o.

19. Summary: Circle: The set of all points in a plane at a given distance from a given point is a circle. P is the set of all points in the plane that are 2 units from P. The given point P is the center of the circle. Radius: The given distance is the radius of the circle. A radius is also a segment joining the center of the circle to a point of the circle. (The plural of radius is radii.) Chord: A segment whose endpoints lie on a circle is a chord. Diameter: A chord that contains the center of a circle is a diameter. A diameter is also the length equal to twice a radius.   P 2

20. Secant: A line that contains a chord of a circle is a secant.   Tangent: A line in the plane of a circle that intersects the circle in exactly one point is a tangent. The point of tangency is the point of intersection. secant diameter radius chord tangent

21. D C M For the circle with center M, BD is a diameter and mCMD = 80°, find each of the following:   1). m CD = ______ 2). m CB = ______ 3) m BMC = ______ 4). m DBC = ______ 5). m CDB = ______ 80° 80° 100° 100° 100° B 280° 260°