Transcript 10.3 Arcs and Chords - St. Monica Catholic Church

10.3 Arcs and Chords
Inscribed: A polygon is inscribed in a circle if each of its vertices lie on the
circle.
Circumscribed: A circle is circumscribed about a polygon if the circle contains
all the vertices of the polygon.
Theorem 10.2
In a circle or in congruent circles, two minor arcs are congruent if and only if
their corresponding chords are congruent.
Theorem 10.3
In a circle, if a diameter (or radius) is perpendicular to a chord, then it bisects the
chord and its arc.
Theorem 10.4
In a circle or in congruent circles, two chords are congruent if and only if they
are equidistant from the center.
TESSELLATIONS The rotations of a tessellation can create twelve congruent central
angles. Determine whether
.
Answer: Since the measures of
are equal,
.
ADVERTISING A logo for an advertising campaign is a pentagon that has five
congruent central angles. Determine whether
.
Answer: no
Circle W has a radius of 10 centimeters. Radius
which is 16 centimeters long.
If
find
is perpendicular to chord
Since radius
is perpendicular to chord
Arc addition postulate
Substitution
Substitution
Subtract 53 from each side.
Answer: 127
Circle W has a radius of 10 centimeters. Radius
which is 16 centimeters long.
Find JL.
is perpendicular to chord
Draw radius

A radius perpendicular to a chord
bisects it.
Definition of segment bisector
Use the Pythagorean Theorem to find WJ.
Pythagorean Theorem
Simplify.
Subtract 64 from each side.
Take the square root of each side.
Segment addition
Subtract 6 from each side.
Answer: 4
Circle O has a radius of 25 units. Radius
which is 40 units long.
a. If
Answer: 145
b. Find CH.
Answer: 10
is perpendicular to chord AE,
Chords
and
If the radius of
are equidistant from the center.
is 15 and EF = 24, find PR and RH.
are equidistant from P, so
.
Draw
to form a right triangle. Use the Pythagorean Theorem.
Pythagorean Theorem
Simplify.
Subtract 144 from each side.
Take the square root of each side.
Answer:
Chords
and
are equidistant from the center of
If TX is 39 and XY is 15, find WZ and UV.
Answer:
Homework:
p. 540 #12-34 evens; 40, 42, 44