thursday, november 14 th
DESCRIPTION
Thursday, November 14 th. Warm Up. Find 1. Z 2. MTRANSCRIPT
Thursday, November 14th
WARM UPFind
1. Z
2. M<U
Homework Answers
Do you know your formulas?!!
P
A
B
Case I: Central Angle: Vertex is AT the center
Central Angle is equal to the ______________
Arc = ___________ the inscribed angle
Angle =
CASE IV. Vertex is OUTSIDE circle
ANGLE
LARGE ARC
small
ARC
small
ARC small
ARC
ANGLE
ANGLE
LARGE ARC
LARGE ARC
Angle =
Tune: If You’re Happy and You Know It
• If the vertex is ON the circle half the arc. <clap, clap>
• If the vertex is INside the circle half the sum. <clap, clap>
• But if the vertex is OUTside, then you’re in for a ride, cause it’s half of the difference anyway. <clap, clap>
Today’s Goal
Secants and tangentsSide Lengths
Segment Lengths in Circles
Find the lengths of segments of chords
Find the lengths of segments of tangents and secants
a
bc
d ab = cd
part part = part part
9
2
6x
x = 3
Solve for x.
Find the length of DB.
8
12 2
x3x
x = 4DB = 20
A
B
C
D
Find the length of each chord.
x = 8AC = 13DB = 14
x5
x - 4
10
A
B
C
D
E A B
C
D
EA • EB = EC • EDoutside whole = outside whole
EA
B
C
D
7 13
4
x
7 (7 + 13) 4(4 + x)=
Ex: 3 Solve for x.
140 = 16 + 4x124 = 4x
x = 31
E
A
B
CD 8
5
6
x
6 (6 + 8) 5(5 + x)=
Ex: 4 Solve for x.
84 = 25 + 5x59 = 5x x = 11.8
E
A
B C
EA2 = EB • ECoutside whole = outside whole
E
A
B C
24
12 x
outside whole = outside whole 242 = 12 (12 + x)576 = 144 + 12x x = 36
Ex: 5 Solve for x.
E
A
B
C15
5
x
outside whole = outside whole x2 = 5 (5 + 15)
x2 = 100x = 10
Ex: 6
Practice Problems