91Ó°ÊÓ

Find $AB.$In Exercise $3,$$\stackrel{¯}{CB}$ is tangent to $⊙A.$

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

a. $m∠AOB=90°$

a. Draw a three large circles and inscribe a different shaped quadrilateral $ABCD$in each.

b. Use a protractor to measure all the angles.

c. Compute $m∠A+m∠C$ and $m∠B+m∠D.$.

d. What is the relationship between opposite angles of an inscribed quadrilateral?

Is there a theorem about spheres related to the theorem in Exercise $12?$ If so, state the theorem.

a. Given:$\stackrel{¯}{WZ}$is a diameter of $⊙o;\stackrel{¯}{OX}âˆ\yen \stackrel{¯}{ZY}$

Prove: $\stackrel{Áåœ}{WX}â‰\dots \stackrel{Áåœ}{XY}.$

(Hint: draw $\stackrel{Áåœ}{OY}.$)

Quad. $ABCD$ is circumscribed about a circle. Discover and prove a relationship between $AB+DC$ and $AD+BC.$

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

d. $m∠AOB=120°$

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.

$\stackrel{¯}{SR}$ is tangent to $⊙P$ and $⊙Q$.

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

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

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

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