1. Learning Target 17
Tangents
Lesson 8-3: Tangents

2. Review: Circle Definition
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
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

4. 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

5. 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

6. THEOREM #1:
If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.
Example:
Find the value of A B C D 4 3 A B C
Lesson 8-3: Tangents

7. THEOREM #2:
If two segments from the same exterior point are tangent to a circle, then they are congruent. B C A
Example:
Find the value of
If AB = 1.8 cm, then AF = 1.8 cm
AE = AF + FE
AE = = 8.8 cm
If FE = 7.0 cm, then DE = 7.0 cm
CE = CD + DE
CE = = 9.4 cm
2.4 cm
1.8
7.0 E A C F B D
Lesson 8-3: Tangents

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. Learning Target #17 b
Arcs
Lesson 8-3: Tangents

10. Lesson 8-1: Circle Terminology
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 8-1: Circle Terminology

11. Lesson 8-1: Circle Terminology
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 8-1: Circle Terminology

12. Lesson 8-1: Circle Terminology
Example: ARCS
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 8-1: Circle Terminology

13. Lesson 8-1: Circle Terminology
Learning Target #17 c
Chords
Lesson 8-1: Circle Terminology

14. Lesson 8-4: Arcs and Chords
Theorem 3:
In a circle, two chords are congruent iff their corresponding minor arcs are congruent. E A B C D
Example:
Lesson 8-4: Arcs and Chords

15. Lesson 8-4: Arcs and Chords
Theorem 4:
In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the chord and its arc. E D A C B
Example:
If AB = 5 cm, find AE.
Lesson 8-4: Arcs and Chords

16. Lesson 8-4: Arcs and Chords
Theorem 5:
In a circle, two chords are congruent if and only if they are equidistant from the center. O A B C D F E
Example:
If AB = 5 cm, find CD.
Since AB = CD, CD = 5 cm.
Lesson 8-4: Arcs and Chords

17. Lesson 8-4: Arcs and Chords
Try Some Sketches:
Draw a circle with a chord that is 15 inches long and 8 inches from the center of the circle.
Draw a radius so that it forms a right triangle.
How could you find the length of the radius?
Solution:
∆ODB is a right triangle and
8cm
15cm O A B D x
Lesson 8-4: Arcs and Chords