10.1 : chords and arcs
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10.1: Chords and Arcs
Obj: _____________________
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Parts of a Circle• Radius: segment from the
center of the circle to a
point on the circle
• Chord: segment whose
endpoints lie on a circle
• Diameter: Chord that contains
the center of the circle
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More Parts Arc: an unbroken part of a circle
Naming Arcs: Name the 2 endpoints and
draw an arc on top
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Semicircle: an arc whose endpoints are
endpoints of a diameter
Naming Semicircles:
Name an endpoint, another pt on arc, other endpt, with arc on tops
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Minor Arcs; Arc that is less than a semicircle
Naming Minor Arcs: Name 2 endpts with arc on top
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Major Arc: More than a semicircle
Naming major arcs: Name endpt,
another pt, other endpt, with arc on top
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Practice• Name the following if P is the center• A) Radius• B) Diameter• C) Chord• D) Semicircle• E) Minor Arc• F) Major Arc
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Even More Parts• Central Angle: angle whose vertex is the
center of the circle
• Intercepted Arc: Arc whose
endpts lie on the sides of
the angle
• Degree Measure of Arcs:
Measure of the central angle
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9.1 Chords and Arcs
Theorems, Postulates, & Definitions
Arc Length:
L =M
360(2r).
Where L= Arc Length M= Deg of central angle r = radius
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Example• Find the arc Length
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Key Skills
9.1 Chords and Arcs
Find central angle measures.
In circle M, find mAMB.
Because 180 + 45 + mAMB = 360, mAMB = 135.
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Key Skills
9.1 Chords and Arcs
Find arc measures and lengths.
In circle M, find mBC
and the length of BC.
mBC = mBMC = 45, so length of
(2)(20) = 15.71 meters.mBC = 45360
TOC
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9.1 Chords and Arcs
Theorems, Postulates, & Definitions
The Converse of the Chords and Arcs Theorem: In a circle, or in congruent circles, the chords of congruent arcs are congruent.
Chords and Arcs Theorem: In a circle, or in congruent circles, the arcs of congruent chords are congruent.
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Practice:
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