Download 1. If the bicycle wheel travels 63 in. in one complete revolution and

CC Geometry 10H
Aim #1: What is the relationship between radii and tangents of circles?
Do Now:
1. If the bicycle wheel travels 63 in. in one complete revolution
0
and rotates only 120 about the center, how far does it travel?
2. If a wheel spoke measures 18 in, what is the circumference
and area of the wheel, to the nearest inch?
center
Definition: A circle is a set of points equidistant from a fixed point, called the _______.
a segment from the center to any point on the circle
Definition: A radius is___________________________________________________.
• All radii of a circle are congruent.
A
O
B
D
C
circles whose diameters (or radii) are equal
Definition: Equal circles are _______________________________________.
congruent
• All radii of equal circles are ___________.
A
B
circle A = circle B
a segment connecting 2 points on the circle's circumference
Definition: A chord is_____________________________________________.
a chord that passes through the center of the circle
Definition: A diameter is________________________________________________.
chord
radius
diameter
twice
• The length of a diameter of a circle is _______________
the length of a radius.
Definition: An arc is a portion of the circumference of a circle.
diameter of a circle.
Definition: A semi-circle is an arc whose endpoints form a _________
than
greater
a semi-circle.
________
Definition: A major arc is an arc that is ___________
minor
arc is an arc that is less than a semi-circle.
Definition: A ___________
Definition:A secant is__________________________________________________.
a line that intersects the circle at 2 points
a line (seg/ray) that intersects the circle at exactly one point
Definition: A tangent is________________________________________________.
where the tangent line and circle intersect
Definition: A point of tangency is__________________________________________.
tangent
secant
point of tangency
Name each figure:
D
E
C
A
O
diameter
center _____
radius _____ _____ _____ secant ______
F
B
H
chord _____ _____
G
I
_____
tangent _____
point of tangency ____
J
A tangent is perpendicular to a radius drawn to the point of
THEOREM: ____________________________________________________________
tangency.
of
tangency
_______________________________________________________________________
A
P
B
P = point of tangency
O
If a line is perpendicular to a radius at the point of
CONVERSE of THEOREM _______________________________________________
intersection on circle, it is a tangent.
______________________________________________________________________
Exercises : Assume the lines that appear tangent are tangent.
3. Find x.
2. Find x.
1. Find x.
L
x
O
O
xo
O
38 0
x
117 0
N
22 0
4. Is XY
6. Find x.
5. Find x.
YV ?
24
Show work to justify
your answer.
12
O
X
8
4
Y
V
x
32
x
8
O
M
8. Find x.
7. Find x.
9
x
O
O
8
560
x0
9. BC = 9, AB = 6, AC = 15. Is BC tangent to circle A? Explain.
10. x = segment joining the centers. Find x,
to the nearest tenth.
9.3
.5
26
2.4
x
11. A belt fits tightly around two circular pulleys as shown. Find the distance
between the centers of the pulleys, to the nearest tenth.
35 in.
14 in.
8 in.
12. Isosceles ΔABC is inscribed in circle O, and base AC is a diameter.
AB = -3x + 61, BC = x - 3 and AC = (x - 3)√2.
a) Draw a labeled diagram
b) Find the perimeter of ΔABC
c) Name the largest angle of ΔABC.
d) Find the length of a radius of circle O.
e) Name a semi-circle of circle O.
f) Name a major arc of circle O.
B
C
Let's Sum it Up!
D
O
E
A
G
F
O = center
= radii
= diameter
= chord, not a diameter
= tangent
C = point of tangency
= secant
= semi-circle
= major arc
= minor arc
Name __________________
Date_________
CC Geometry H
HW #1
1. Name, in symbolic form:
C
a) a diameter _________
F
B
b) a tangent _____
O
A
c) a chord _______
G
d) a secant _______
D
e) a right angle ______
E
f) two complementary angles _____ _____
2a) Find x.
b) Find x.
c) Find x ,to the nearest tenth.
15
7
24
O
x
9
10 cm
x
7 cm
x
3. In circle O, diameter
AB = 3x + 11 and diameter
CD = 5x - 23.
Find the length of a radius.
4. In circle O, radius
2
OA = x + 16 and radius
OB = 4x + 48. Find
all possible lengths of a
diameter.
5. D and E are points of tangency.
Radius AE = 5 cm, CD = 12 cm.
a) Find CA.
D
12 cm
A
C
5 cm
b) By what congruence criteria is ΔCDA ≅ ΔCEA?
E
c) What is true about m≮DCA and m≮ECA? Why?
6. Find x, the length of the common tangent segment between the two circles
(nearest hundredth).
x
G
5
4
3
H
Review
7. Find the perimeter of the triangle to the nearest tenth.
1050
300
10
8. The larger cone has a similar smaller cone with half its radius inside.
What fraction of the larger cone's volume is outside the smaller cone?
9. If sin θ =
, find cos θ and tan θ.
THE "PERFECT" CIRCLE?
http://www.youtube.com/watch?v=eAhfZUZiwSE
What is the definition of a circle?