7.3 Notes – Central and Inscribed Angles
Arc Measure and Length
Name: _______________________
Arc Classification:
Minor Arc:
part of the circle’s edge measuring less than _________.
notation: named by endpoints
Major Arc:
part of the circle’s edge measuring more than _________, but less than _________.
notation: named by endpoints AND another point on the arc
Semicircle:
part of the circle’s edge measuring exactly _________.
notation: named by endpoints AND another point on the arc
1.
Name the type of arc shown in bold.
2.
3.
There are two types of angles in a circle; it is important that you know the difference between them:
1. A central angle (an angle whose vertex is at the center of the circle).
̂)
A central angle equals m(𝑨𝑹𝑪
2. An inscribed angle (an angle whose vertex is on the edge of the circle).
𝟏
̂)
An inscribed angle equals 𝟐m(𝑨𝑹𝑪
Angles in semicircles:
If 𝐶𝐷 is a diameter of ⊙ 𝑃, what is the measure of ∡𝐶𝐴𝐷? Why?
Therefore, the angle inscribed in a semicircle is always _______________________.
̂ = 72°, and 𝑚∡𝐶𝑃𝐷 = 144°. Find each measure indicated.
In ⊙ 𝑃, 𝑚∡𝐴𝑃𝐵 ≅ 𝑚∡𝐵𝑃𝐷, 𝑚𝐵𝐷
1. 𝑚∡𝐷𝐴𝐵 = ___________
̂ = ___________
2. 𝑚𝐶𝐷
̂ = ___________
3. 𝑚𝐴𝐵
̂ = ___________
4. 𝑚𝐴𝐶
̂ = ___________
5. 𝑚𝐶𝐷𝐴
6. 𝑚∡𝐶𝑃𝐴 = ___________
For each of the following, find the indicated measure.
𝑚∡𝐴𝑃𝐵 = ___________
1.
2.
̂ = ___________
𝑚𝐶𝐴
𝑚∡𝐵𝑃𝐶 = ___________
̂ = ___________
𝑚𝐶𝐷
̂ = ___________
𝑚𝐴𝐵
̂ = ___________
𝑚𝐴𝐷
̂ = ___________
𝑚𝐵𝐶
̂ = ___________
𝑚𝐴𝐵𝐶
̂ = ___________
𝑚𝐴𝐵𝐶
̂ = ___________
𝑚𝐵𝐶
𝑚∡𝐴𝐵𝐶 = ___________
𝑚∡𝐶𝐵𝐷 = ___________
̂ = ___________
𝑚𝐴𝐷𝐶
𝑚∡𝐵𝐴𝑄 = ___________
An arc is a portion of the edge of a circle and can be:

measured in degrees,
notation:
̂ , _____ ___________
𝒎𝑨𝑩

measured in length,
notation:
̂ , _____ ___________
𝑨𝑩
How is finding the arc length different from finding the arc measure?
__________________________________________________________________________________________
__________________________________________________________________________________________
What is the formula for finding the length of an arc?
̂) =
Length (𝑨𝑹𝑪
Find the measure and arc length indicated:
̂ = ______________
1.
𝑚𝐹𝐻
̂ = ______________
𝐹𝐻
· ________
2.
̂ = ______________
𝑚𝐴𝐶𝐵
̂ = ______________
𝐴𝐶𝐵