Circles

1
Circles

• Chapter 10
• Sections 10.1 10.7

2
secant
tangent
point of tangency
3
Secant segment
B
A
C
4
Secant segment
B
A
C
5
Tangent segment
B
A
6
Tangent Theorems

• Tangent is perpendicular to a radius at the point
  of tangency.

Create right triangles for problem solving.
7
Tangent Theorems
A
B

• Two tangent segments from the same point are
  congruent.

C
8
Arcs and Angles

• There are three possible arc/angle situations.
• Vertex located ON THE CIRCLE.
• Vertex located IN THE CIRCLE.
• Vertex located OUTSIDE THE CIRCLE.

9
Vertex ON THE CIRCLE
angle ½ arc
250
110
55
125
10
Vertex IN THE CIRCLE
angle ½(110 130)
110
½(240)
120
120
130
angle ½(arc arc)
11
Vertex OUTSIDE THE CIRCLE
12
Vertex OUTSIDE THE CIRCLE
angle ½(150 - 50)
½(100)
50
150
50
angle ½(lg. arc sm. arc)
13

• Vertex ON THE CIRCLE
• angle ½ arc
• Vertex IN THE CIRCLE
• angle ½(arc arc)
• Vertex OUTSIDE THE CIRCLE
• angle ½(lg. arc sm. arc)

14
Segment Relationships

• There are three possible situations.
• Two chords
• Two secant segments
• A tangent and a secant segment

15
Two chords
The product of the segment parts are ?.
A
C
P
B
D
APPB
CPPD

16
Two Secant Segments
A
The products of the secant and the external
secant are .
P
C
B
D
ABAP
ADAC

17
Tangent and Secant Segment
A
The tangent squared the product of the secant
and the external secant.
P
C
B
ACAC
ABAP

18
partpart partpart
wholeoutside wholeoutside
tangenttangent wholeoutside
19
Test 10.5-10.7 Total problems33

• Multiple choice (15)
• Individual diagrams (18)
• Tangent theorems (6)
• Arcs/Angles (6)
• Secant segments/tangents (6)