10.1 : chords and arcs

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10.1: Chords and Arcs

Obj: _____________________

___________________________


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


More Parts Arc: an unbroken part of a circle

Naming Arcs: Name the 2 endpoints and

draw an arc on top


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


Minor Arcs; Arc that is less than a semicircle

Naming Minor Arcs: Name 2 endpts with arc on top


Major Arc: More than a semicircle

Naming major arcs: Name endpt,

another pt, other endpt, with arc on top


Practice• Name the following if P is the center• A) Radius• B) Diameter• C) Chord• D) Semicircle• E) Minor Arc• F) Major Arc


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


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


Example• Find the arc Length


Key Skills

9.1 Chords and Arcs

Find central angle measures.

In circle M, find mAMB.

Because 180 + 45 + mAMB = 360, mAMB = 135.


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


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.


Practice:

10.1 : chords and arcs

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