1. 11.notebook September 19, 2012
Objective: Circles, Properties of Circles, Quadratic Formula
Radius Chord Diameter Tangent
Central Angle arc formed by two radii connecting the
endpoints of the arc with the center of the circle
B C
minor arc BC
major arc BAC
A
measure of central angle = measure of arc (not length of arc)
1
2. 11.notebook September 19, 2012
Measure of central angle
43o same as measure of arc
2
3. 11.notebook September 19, 2012
inscribed angle an angle whose vertex lies on a circle
and whose sides are chords of the circle
o
44
o
22
measure of inscribed angle = 1/2 measure of arc
3
4. 11.notebook September 19, 2012
B
o
The sum of any pair of opposite angles = 180
C
A
D
When two chords intersect, the product of the lengths of the segments of one
chord equals the product of the lengths of the segments of the other chord.
x xy = pq x x =
p
q q q y
p p
A y
y
B
4
5. 11.notebook September 19, 2012
Two tangent segments from a point outside a circle have equal lengths
m
P
n
5
6. 11.notebook September 19, 2012
1. Find x and y.
A
o
30
P 46
o
(x + 10)o (y + 20)o
R B
6
7. 11.notebook September 19, 2012
2. Find x, y, and z.
o
z
o
75
o
x
o
80 o
y
7
8. 11.notebook September 19, 2012
3. Find x, y, and z.
o o
z o x
35
o
75
o
y
8
9. 11.notebook September 19, 2012
4. Find x.
15
20
x + 10
x + 5
9
10. 11.notebook September 19, 2012
5. The triangle and the circle are tangent at three points, as shown. Find x and y.
x + y
x + 4
10
6
x x
10
11. 11.notebook September 19, 2012
Quadratic Formula.
Derive the quadratic formula using completing the square.
ax2 + bx + c = 0
11
12. 11.notebook September 19, 2012
6. Use the quadratic formula to find the roots of the equation 3x2 2x + 5 = 0.
12
