91Ó°ÊÓ

Use a compass to draw a large $⊙o.$Draw a central $∠AOB.$.

a. draw three other points $P,Q$and $R$ that are on $⊙o$but not on $\stackrel{Áåœ}{AB}$.

then draw $∠APB,∠AQB$ and $∠ARB$.

b. Use a protractor to find $m∠AOB,m∠APB,m∠AQB$ and $m∠ARB$.

c. What is the relationship between $m∠APB,m∠AQB$ and $m∠ARB?$

What is the relationship between $m∠AOB$and $m∠APB?$

Discover and prove a theorem about two lines tangent to a circle at the endpoints of a diameter.

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 $\stackrel{¯}{AB}$.

b. $m∠AOB=180°$

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

In exercises $8-13$ find the angle or the arc named.

$\stackrel{Áåœ}{EHF}$

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?

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 $\stackrel{¯}{AB}$.

c.$m∠AOB=60°$

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 $\stackrel{Áåœ}{OY}.$)

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. $m∠AOB=120°$