McDougal Littell Jurgensen Geometry : Student Edition 2000

Ray C. Jurgensen, Richard G. Brown

Chapter 9

Circle - all with Video Answers

Educators

Section 1

Basic Terms

Problem 1

Draw a circle and several parallel chords. What do you think is true of the midpoints of all such chords?

Amrita Bhasin

Amrita Bhasin

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Problem 2

Draw a circle with center $O$ and a line $\overleftarrow{T S}$ tangent to $\odot O$ at $T .$ Draw $\overline{O T}$, and use a protractor to find $m \angle O T S$.

Georgiann Andersen

Georgiann Andersen

Numerade Educator

Problem 3

a. Draw a right triangle inscribed in a circle.
b. What do you know about the midpoint of the hypotenuse?
c. Where is the center of the circle?
d. If the legs of the right triangle are 6 and $8,$ find the radius of the circle.

Amrita Bhasin

Numerade Educator

Problem 4

Plane $Z$ passes through the center of sphere $Q$.
a. Explain why $Q R=Q S=Q T$
b. Explain why the intersection of the plane and the sphere is a circle. (The intersection of a sphere with any.plane passing through the center of the sphere is called a great circle of the sphere.)

Georgiann Andersen

Georgiann Andersen

Numerade Educator

Problem 5

The radii of two concentric circles are $15 \mathrm{cm}$ and $7 \mathrm{cm} .$ A diameter $\overline{A B}$ of the larger circle intersects the smaller circle at $C$ and $D .$ Find two possible values for $A C$

Amrita Bhasin

Numerade Educator

Problem 6

For each exercise draw a circle and inscribe the polygon in the circle.
A rectangle

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Georgiann Andersen

Numerade Educator

Problem 7

For each exercise draw a circle and inscribe the polygon in the circle.
A trapezoid

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Problem 8

For each exercise draw a circle and inscribe the polygon in the circle.
An obtuse triangle

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Georgiann Andersen

Numerade Educator

Problem 9

For each exercise draw a circle and inscribe the polygon in the circle.
A parallelogram

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Numerade Educator

Problem 10

For each exercise draw a circle and inscribe the polygon in the circle.
An acute isosceles triangle

Georgiann Andersen

Georgiann Andersen

Numerade Educator

Problem 11

For each exercise draw a circle and inscribe the polygon in the circle.
A quadrilateral $P Q R S$. with $\overline{P R}$ a diameter

Amrita Bhasin

Numerade Educator

Problem 12

For each exercise draw $\odot O$ with radius $12 .$ Then draw radii $\overline{O A}$ and $\overline{O B}$ to form an angle with the measure named. Find the length of $\overline{A B}$.
$$m \angle A O B=90$$

Georgiann Andersen

Georgiann Andersen

Numerade Educator

Problem 13

For each exercise draw $\odot O$ with radius $12 .$ Then draw radii $\overline{O A}$ and $\overline{O B}$ to form an angle with the measure named. Find the length of $\overline{A B}$.
$$m \angle A O B=180$$

Amrita Bhasin

Numerade Educator

Problem 14

For each exercise draw $\odot O$ with radius $12 .$ Then draw radii $\overline{O A}$ and $\overline{O B}$ to form an angle with the measure named. Find the length of $\overline{A B}$.
$$m \angle A O B=60$$

Georgiann Andersen

Georgiann Andersen

Numerade Educator

Problem 15

For each exercise draw $\odot O$ with radius $12 .$ Then draw radii $\overline{O A}$ and $\overline{O B}$ to form an angle with the measure named. Find the length of $\overline{A B}$.
$$m \angle A O B=120$$

Amrita Bhasin

Numerade Educator

Problem 16

Draw two points $A$ and $B$ and several circles that pass through $A$ and $B$. Locate the centers of these circles. On the basis of your experiment. complete the following statement:
The centers of all circles passing through $A$ and $B$ lie on Write an argument to support your statement.

Georgiann Andersen

Georgiann Andersen

Numerade Educator

Problem 17

$\odot Q$ and $\odot R$ are congruent circles that intersect at $C$ and $D . \overline{C D}$ is called the common chord of the circles.
a. What kind of quadrilateral is $Q D R C ?$ Why?
b. $\overline{C D}$ must be the perpendicular bisector of $\overline{Q R}$. Why?
c. If $Q C=17$ and $Q R=30$, find $C D$.
(IMAGE CAN'T COPY)

Amrita Bhasin

Numerade Educator

Problem 18

Draw two congruent circles with radii 6 each passing through the center of the other. Find the length of their common chord.

Georgiann Andersen

Georgiann Andersen

Numerade Educator

Problem 19

$\odot P$ and $\odot Q$ have radii 5 and 7 and $P Q=6 .$ Find the length of the common chord $\overline{A B}$. (Hint: $A P B Q$ is a kite and $\overline{P Q}$ is the perpendicular bisector of $\overline{A B}$. See Exercise 28 , page $193 .$ Let $N$ be the intersection of $\overline{P Q}$ and $\overline{A B},$ and let $P N=x$ and $A N=y .$ Write two equations in terms of $x$ and $y .$ )
(IMAGE CAN'T COPY)

Amrita Bhasin

Numerade Educator

Problem 20

Draw a diagram similar to the one shown, but much larger. Carefully draw the perpendicular bisectors of $\overline{A B}$ and $\overline{B C}$.
a. The perpendicular bisectors intersect in a point. Where does that point appear to be?
b. Write an argument that justifies your answer to part (a).
(IMAGE CAN'T COPY)

Georgiann Andersen

Georgiann Andersen

Numerade Educator