Title: Arcs
19-3
Arcs Chords
Pg 459-465
Wednesday, November 18, 2009
2What You'll Learn
To recognize and us relationships among arcs,
chords, and diameters.
Why It's Important
You can use arcs and chords to solve problems
involving geology.
3Vocabulary
- Arc of the chord When a minor arc and a chord
share the same endpoints. - Theorem 9-1 In a circle or in congruent
circles, two minor arcs are congruent if and only
if their corresponding chords are congruent.
AB CD EF
4Vocabulary
- A polygon is an inscribed polygon if each of its
vertices lies on a circle. - Theorem 9-2 In a circle, if a diameter is
perpendicular to a chord, then it bisects the
chord and its arc.
5Vocabulary
- Theorem 9-3 In a circle or in congruent
circles, two chords are congruent if and only if
they are equidistant from the center.
AB CD
6Examples
A stop sign is an octagon with congruent sides.
It can be inscribed in a circle by using the
center of the sign and a vertex of the sign as
endpoints for the radius of the circle, as in
QR. Find the measure of each of the eight
corresponding arcs of a circle around the stop
sign shown at the right.
R
STOP
Q
7Examples
Suppose a chord of a circle is 10 inches long and
12 inches from the center of the circle. Find the
length of the radius.
8Assignment Page 462 13 39 odd 47 56 all