1. Bell Ringer 4-8-19 Write an example of each of the following:
1. Radius
2. Secant
3. Tangent
4. Chord
5. Diameter
6. Minor arc
7. Major arc
8. Central angle
9. Inscribed angle
10. Center

2. Arc Length
Monday, April 8, 2019

3. Quick Definition Review
Chord: a segment whose endpoints lie on a circle A B AB

4. Quick Definition Review
Arc: an unbroken part of a circle

5. Quick Definition Review
Minor Arc: an arc that is less than half of a circle.
to name, use 2 points

6. Quick Definition Review
Major Arc: an arc that is more than half of a circle.
to name, use 3 points

7. Quick Definition Review
Central Angle: an angle whose vertex is at the center of a circle

8. Quick Definition Review
Inscribed Angle: an angle whose vertex is on a circle and whose sides are chords of the circle

9. Quick Definition Review
Tangent: a line, ray, or segment that intersects the circle in only one point (perpendicular)

10. Quick Definition Review
Secant: a line, ray, or segment that contains a chord

11. Arc Measure & Arc Length
Remember:
𝒎 𝑪𝒆𝒏𝒕𝒓𝒂𝒍 ∠=𝒎 𝒊𝒏𝒕𝒆𝒓𝒄𝒆𝒑𝒕𝒆𝒅 𝑨𝒓𝒄
Arc Measure is in degrees;
Arc Length is in units like cm, ft, and in.
The central angle is a portion of the total degrees in a circle whereas Arc Length is a portion of the circumference.
𝑨𝒓𝒄 𝑴𝒆𝒂𝒔𝒖𝒓𝒆 𝟑𝟔𝟎 = 𝑨𝒓𝒄 𝑳𝒆𝒏𝒈𝒕𝒉 𝑪𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆
Everything in circles is proportional!

12. Examples Find the arc length: 1. Radius 5 cm, central angle 50º
Find the circumference:
3. Central angle 55º, arc length 5.5 cm
4. Central angle 60º, arc length 3.82 m
Find the central angle:
5. Arc length 45 ft, radius 12 ft
6. Arc length 30in, radius 14 in

13. Classwork Homework Geometry book p. 686-688 #13-47 odd
Circumference and Arc Length

14. Exit Ticket
1. How does a central angle compare to its intercepted arc?
2. What is the difference between arc length and arc measure?
3. What proportion can you use with respect to arc measure and arc length?