ARCS An ARC is any unbroken part of the circumference of a circle. It is named using its ENDPOINTS.


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1 ARCS An ARC is any unbroken part of the circumference of a circle. It is named using its ENDPOINTS. A B X Z Y A MINOR arc is LESS than 1/2 way around the circle. A MAJOR arc is MORE than 1/2 way around the circle. We also use a point on the arc to name it. This is arc XYZ.
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3 Central and Inscribed on the Same Arc A B Minor Arc AB measures 80. The measure of AZB is 80. The measure of AXB is 40. Z The measure of major arc AXB is 260. What do minor arc AB and major arc AXB add up to? X
4 Central Angle Z Y ZYX is a CENTRAL ANGLE. What are the characteristics of a central angle? X Answer: A CENTRAL ANGLE is an angle whose vertex is the centerpoint of the circle.
5 Chord vs. Secant vs. Diameter MN is a CHORD. Y XY is a secant. AB is a diameter. How are they the same? A M N B How are they different? X Answer: The diameter goes all the way from one side of the circle, through the centerpoint, to the other side of the circle. It is a LINE SEGMENT. A chord is a line segment that has endpoints on the perimeter of the circle. It may or may not go through the centerpoint. A secant is a line (not a line segment) that intersects the circle at exactly 2 points, and goes on forever. It may or may not pass through the centerpoint.
6 Diameter vs. Radius AB is the DIAMETER of circle C. CQ is the RADIUS of circle C. What is the difference between the DIAMETER and the RADIUS? How are they the SAME? A C Q B What is the relationship between their lengths? Answer: The diameter goes all the way from one side of the circle, through the centerpoint, to the other side of the circle. They are the same because they both intersect the centerpoint of the circle. The diameter is ALWAYS twice as long as the radius. The radius starts at the center and ends at ANY point on the circumference (perimeter) of the circle. The diameter starts anywhere on the circumference and goes straight across through the center to the other side.
7 Inscribed Angle ABC is an INSCRIBED ANGLE. What are the characteristics of an INSCRIBED ANGLE? A C B Answer: An INSCRIBED ANGLE is an angle whose vertex is on the perimeter of a circle.
8 Tangent vs. Secant XY is a secant. D Y BD is a tangent. How are they the same? B How are they different? X Answer: A secant intersects the circle at exactly 2 points on the perimeter and extends forever in either direction. A tangent intersects the circle at exactly 1 point on the perimeter and is PERPENDICULAR to the radius at that point.
9 Name: Lines in a Circle, U6D1 Date: Period: 1. Use the circle to answer each question a. We use the CENTERPOINT of a circle to name the circle. What is the name of the circle to the right? b. Use a straightedge to draw OB, a RADIUS of circle O. Where are the endpoints of the RADIUS located with respect to the circle? c. How many RADII (the plural of radius) does a circle have? Explain how you know. d. Use a straightedge to draw AC. Then, use a straightedge to draw BD. How are the line segments the same? How are they different? e. Why is BD not considered a DIAMETER? f. The proper name for BD is. g. How does the length of the DIAMETER of a circle relate to the length of the RADIUS? h. The RADII of the same circle, or of congruent circles are sometimes/always/never congruent. Explain your choice. 2. A SECANT of a circle is a line that. 3. Draw a secant using the CIRCLE Z. 4. A CHORD of a circle is a line segment that. 5. Maribel says that a CHORD is part of a SECANT. David says that a CHORD is different from a SECANT. Explain why Maribel and David are both correct. 6. What is the longest chord in any circle? (Hint, the answer is NOT a number). 7. A TANGENT of a circle is a. is called the POINT OF TANGENCY. 8. Draw a TANGENT anywhere on circle Z. 9. Choose another point on the circle. How many TANGENT lines can you draw through this point? 10. Explain the difference between a SECANT and a TANGENT.
10 Name: Angles in a Circle, U6D1 Date: Period: 1. A CENTRAL ANGLE is. 2. An INSCRIBED ANGLE. 3. An ARC of a circle is. An ARC is named using its. 4. A MAJOR ARC of a circle is the. It goes more than halfway around a circle. 5. A MINOR ARC of a circle is. It goes less than halfway around a circle. 6. A SEMI CIRCLE is exactly of a circle. 7. Now, go look for the picture with CENTRAL and INSCRIBED angles on it. Use this space to explain the difference between a CENTRAL and INSCRIBED angle Is CPD a CENTRAL angle or an INSCRIBED angle? What is the relationship between the measure of the angle and the ARC it intercepts? 10. What is the relationship between the ARC it intercepts and the major ARC? 11. Is ONM a CENTRAL angle or an INSCRIBED angle? 12. What is the relationship between ONM and arc OM? 13. What is the relationship between arc OM and arc ONM? 14. From questions 7 through 14, what can you conclude about CENTRAL angles? Consider a CENTRAL angle and an INSCRIBED angle that INTERCEPT the same ARC. What is the relationship between the measure of these two angles?. 16. Label the three pictures below with the TYPE(S) of angle and ALL of the missing ARC/ANGLE measures.
11 Name: Homework, U6D1 Date: Period: Use the circle above to answer these questions. 1. Name a diameter of the circle. 2. Name a radius. 3. Name a central angle. 4. Name an inscribed angle. 5. Name a minor arc. 6. Name a major arc. 7. Name a semicircle. 8. Name a tangent. 9. Name a secant. 10. Name a chord. Instructions: For the rest of this homework sheet, make sure to label the measure of EVERY ANGLE and ARC on EVERY PROBLEM. (16z +12) (6x 20) (2z +4) (5x +5) (4x +20)
12 If AB is a diameter, find the measure of ACB. Then, find the value of x.
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