Chapter 9: Circles

For each exercise draw $\odot O$ with radius $12$. Then draw radii $\overline{OA}$ and to $\overline{OB}$ form an angle with the measure named. Find the length of $\overline{AB}$.

d. $m\angle AOB=120°$

$\overline{PA}$, $\overline{PB},$and $\overline{RS}$ are tangents.

Explain, Why $PR+RS+SP=PA+PB.$

Draw two points $A$ & $B$ 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.

$\overline{SR}$ is tangent to $\odot P$ and $\odot Q$.

$QT=6,TR=8,PR=30.$

$PQ=?,PS=?,ST=?$

$\odot \mathbf{Q}$ and $\odot \mathbf{R}$ are congruent circles the intersect at $\mathbf{C}$ and$\mathbf{D}$. $\overline{\mathbf{CD}}$ is called the common chord of the circles.

1. What kind of quadrilateral is $\mathbf{QDRC}$? Why?
2. $\overline{\mathbf{CD}}$Must be the perpendicular bisector of $\odot \mathbf{Q}$. Why?
3. If $QC=17$ and $QR=30$, find $CD$.

$\overline{JK}$ is tangent to $\odot P$ and $\odot Q$.

$JK=?$

In Exercises 17-20, the latitude of a city is given. Sketch the earth and a circle of latitude through the city. Find the radius of this circle.

Milwaukee, Wisconsin; $43°N$

Drawtwo congruent circles with radii $\mathbf{6}$ each passing through the centre of other and to find length of their common chord.

In Exercises 17-20, the latitude of a city is given. Sketch the earth and a circle of latitude through the city. Find the radius of this circle.

Columbus, Obie; $40°N$