February 18, 2016
Name: ______________________
What is the area of the shaded region if r = 4? Leave your answer
as an expression in terms of π .
_______________
February 18, 2016
Name: ______________________
What is the area of the shaded region if r = 4? Leave your answer
as an expression in terms of π .
_______________
February 18, 2016
February 18, 2016
(10.3) Arcs and Chords
Objective: To recognize and use the relationships between arcs and
chords.
Why: The relationships between arcs and chords can help us find
measures.
February 18, 2016
Obj: To recognize and use the relationships between arcs and chords.
chord: segment with endpoints on the circle
February 18, 2016
Obj: To recognize and use the relationships between arcs and chords.
Theorem: In the same circle or congruent circles, two arcs are
congruent IFF their corresponding chords are congruent.
B
A
C
D
Proof:
Statement
Reason
February 18, 2016
Obj: To recognize and use the relationships between arcs and chords.
February 18, 2016
Obj: To recognize and use the relationships between arcs and chords.
Theorems:
If a diameter (or radius) is perpendicular to a chord, then it
bisects the chord.
A
C
D
B
The perpendicular bisector of a chord is a diameter (or radius)
of the circle.
A
C
D
B
February 18, 2016
135
24°
February 18, 2016
Obj: To recognize and use the relationships between arcs and chords.
How to find the center of a circle:
0°
0
February 18, 2016
Find ST.
Obj: To recognize and use the relationships between arcs and chords.
February 18, 2016
Obj: To recognize and use the relationships between arcs and chords.
Theorem:
In the same circle or congruent circles, two chords are congruent
IFF they are equidistant from the center.
B
E
O
A
D
C
F
February 18, 2016
Obj: To recognize and use the relationships between arcs and chords.
February 18, 2016
Obj: To recognize and use the relationships between arcs and chords.
HW:
(HR) Pg.719: 7-15odd, 16-20, 24, 26, 27, 31, 35
February 18, 2016
Obj: To recognize and use the relationships between arcs and chords.