Chapter 10
Circles
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Chapter 10 Learning Targets (KRSP):
I can……
1. Understand circle vocabulary and be able to draw examples;
2. Distinguish, draw and solve different types of tangents;
3. Locate different types of arcs and find their measurement;
4. Use properties of chords to finding measurements;
5. Find the measures of single and multiple inscribed angles, along with various other angles in a circle;
6. Solve for missing segments in a circle by identifying the property and relationship it follows;
7. Write the equation of and graph circles.
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Learning Target #1
Understand circle vocabulary and be able to draw examples
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Circles
center
"circle P" or OP
(d)
r
diamete
P
radius (r)
Note: d = 2r
Interior of a Circle
Exterior of a Circle
­ points inside the circle
­ points outside the circle
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Chords
R
Q
P
chord
diameter = chord that passes thru the center
segment whose endpoints
are points on the circle
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Secants v s. Tangents
tangen
t
point of
tangency
C
line that intersects circle at exactly 1 point
k
radius is at point of
tangency
m
secant
line that intersects the
circle at 2 points
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Intersections
2 pts. of intersection
1 pt. of intersection
(tangent circles)
internally tangent
externally tangent
common tangent
common internal tangent
­ tangent intersects segment that joins centers of the 2 circles
common external tangent ­ tangent does not intersect segment that joins centers
0 pts. of intersection
concentric circles
common center
­
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ex: Tell whether the internal
a. A
common tangents are external or b. B
C
D
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Arcs
C
minor arc ­
central angle is
less than 180
major arc ­
central angle
is >180 , but < 360
A
T
central
angle­
vertex
at center
B
semicircle ­ endpoints of arc are endpoints of diameter
Naming Arcs
minor arc­ named by endpoints
major arc/semicircle­ named by endpoints and a point on the arc
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Inscribed Angle/Intercepted Arc
A
inscribed angle ­
vertex on edge of circle, sides contain
chords
B
intercepted arc ­
arc on interior
of inscribed angle
P
C
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ASSIGNMENT
p. 599 #18­28
p. 607 #12­19
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