geo circle vocab.notebook
April 04, 2013
Aim:What are the parts of a circle?
Terms and Vocabulary:
Do­Now:
Which do you think is a better illustration of a circle: a round pizza or a bicycle tire? Explain the reasons for your choice.
Circle: The set of all points in a plane that are equidistant from a fixed point called the center.
Radius: A segment whose endpoints are the center of a circle and a point on the circle. (All radii of the same circle are congruent ).
Chord: A segment whose endpoints are 2 points on a circle.
Diameter: A chord that passes through the center of a Circle.
O
Secant: A line that intersects a circle in two points
Tangent: A line that intersects a circle in exactly one point.
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geo circle vocab.notebook
April 04, 2013
Circles with the same center are
called Concentric Circles circles.
Circumference: Distance around a circle. The perimeter of a circle.
Congruent Circles: have congruent radii.
Arc of a circle: An arc is part of a circle's circumference.
OQ PA
Q
O
P
A
A minor arc has a measure that is less than 180 . (We name a minor with 2 letters.)
A major arc has a measure that is greater than 180 . We name a major arc with 3 letters.
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geo circle vocab.notebook
A semicircle is an arc whose endpoints are the endpoints of a diameter.
It has a measure of 180 . We name a semicircle with 3 letters.
April 04, 2013
Central Angle: An angle whose vertex is the center of a circle.
Inscribed Angle: An angle whose vertex is a point on a circle and whose sides contain chords
In circle O:
T
A
B
O
Q
M
N
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geo circle vocab.notebook
April 04, 2013
Aim: How can we find arc length and arc degrees of a circle?
T
Do­Now: Name:
(a) tangent
(b) secant
(c) chord
(d) radius
(e) diameter
(f) central angle (g)inscribed angle.
(h) Major arc
(i) Minor arc
5 cm
What is the degree measure of a circle?
O
What is the circumference of this circle?
J
A
B
O
Q
M
N
Def:
In a circle, the degree measure of an arc is equal to the measure of the central angle that intercepts the arc.
O
C
Ex) Find the degree measure of arc ACB.
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geo circle vocab.notebook
Find:
(a) Find mAB
April 04, 2013
How can we find the arc length?
A
In a circle, the length of an arc is a portion of the circumference
C
(b) the measure of CEB if <COB=195.
O
71
B
E
(c) Find the degree measure of central angle AOC if mAC =99.
arc length arc measure
=
circumference
360
central angle
circumference
arc length = 360
arc length = θ
2
360 πr
arc length = θ
360 2πr
Ex) In circle O, the radius is 8, and the measure of minor arc is 110 degrees. Find the length of minor arc. Leave your answer in terms of π.
In circle O, the radius is 4, and the measure of minor arc is 120 degrees. (A) Find the length of minor arc. Leave your answer in terms of π.
(B) Find the length of major arc. Leave your answer in terms of π.
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geo circle vocab.notebook
Find the radius of a circle in which an arc which contains 270 degrees has a length of 18π.
What is the length of the arc from her dog house to the hydrant, following minor arc , to the nearest foot.
April 04, 2013
In circle O, the radius is 4, and the length of minor arc is 4.2 feet. Find the measure of minor arc to the nearest degree.
Alison is jogging on a circular track that has a radius of 140 feet. She runs along the track from point R to point N, a distance of 230 feet. Find to the nearest degree, the measure of minor arc . 6