1. Lesson 8-1: Circle Terminology

2. Lesson 8-1: Circle Terminology
Circle Definition
Circle :
The set of points coplanar points equidistant from a given point.
The given point is called the CENTER of the circle.
The distance from the center to the circle is called the RADIUS.
Center
Radius
Lesson 8-1: Circle Terminology

3. Lesson 8-1: Circle Terminology
Definitions
Chord :
The segment whose endpoints lie on the circle.
Diameter :
A chord that contains the center of the circle.
Tangent :
A line in the plane of the circle that intersects the circle in exactly one point.
Tangent
Point of Tangency :
Chord
The point where the tangent line intersects the circle.
Diameter
Secant :
A line that contains a chord.
Secant
Lesson 8-1: Circle Terminology

4. Lesson 8-1: Circle Terminology
Example: In the following figure identify the chords, radii, and diameters.
Chords: O D A B F C E
Radii:
Diameter:
Lesson 8-1: Circle Terminology

5. Lesson 8-1: Circle Terminology
Definitions
Congruent Circles :
Circles that have congruent radii. 2 2
Concentric circles :
Circles that lie in the same plane and have the same center.
Lesson 8-1: Circle Terminology

6. Lesson 8-1: Circle Terminology
CIRCUMFERENCE:
Circumference is the distance around the circle.
Formula: Or
where
Example:
Find the circumference of the following circle.
3 cm cm
Lesson 8-1: Circle Terminology

7. Lesson 8-1: Circle Terminology
Examples:
1) Find the circumference of a helipad if it has a diameter of 79 feet.
2) Find the circumference of each circle described. Round to the nearest hundredth
a) radius=2.5 cm b) diameter=16ft
Lesson 8-1: Circle Terminology

8. Lesson 8-1: Circle Terminology
Polygons
Inscribed Polygon:
A polygon inside the circle whose vertices lie on the circle.
Circumscribed Polygon :
A polygon whose sides are tangent to a circle.
Lesson 8-1: Circle Terminology

9. ARCS
Arcs :
The part or portion on the circle from some point B to C is called an arc. A B C
Example: B
Semicircle:
An arc that is equal to 180°. O A
Example: C
Lesson 8-2: Formulas

10. Central Angle
A central angle is an angle whose vertex is at the center of the circle.
The arc measure is written as m BC
The measure of a minor arc is the measure of its central angle.
The measure of a major arc is 360 minus the measure of its central angle.
Lesson 8-2: Formulas

11. Minor Arc & Major Arc Minor Arc :
A minor arc is an arc that is less than 180°
A minor arc is named using its endpoints with an “arc” above. A
Example:
Major Arc:
A major arc is an arc that is greater than 180°. B B O
A major arc is named using its endpoints along with another point on the arc (in order). A
Example: C
Lesson 8-2: Formulas

12. Example: ARCS Minor Arc: Major Arc: Semicircle:
Identify a minor arc, a major arc, and a semicircle, given that is a diameter.
Minor Arc: A C D E F
Major Arc:
Semicircle:
Lesson 8-2: Formulas

13. Adjacent Arcs
Adjacent arcs-arcs in a circle that have exactly one point in common.
BC and CD are adjacent arcs
Lesson 8-2: Formulas

14. Arc Length Arc length is the distance around an arc. Formula:
The circumference multiplied by the ratio of the center angle and 360°.
Example:
Arc Length 4 cm 72 B C A
Lesson 8-2: Formulas

15. Examples: Find the Arc length. Round to the nearest hundredth. 1) 2)
1) 2)
Lesson 8-2: Formulas