Chapter 9: Circles

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.

Find $AB.$In Exercise $3,$$\overline{CB}$ is tangent to $\odot A.$

Find the number of odd and even vertices in each network. Imagine travelling each network to see if it can be traced without backtracking.

$\overline{JT}$is tangent to $\odot$$O$at $T$. Complete.

If $m\angle TOJ=60$ and $OT=6$, then $JO=?$

a. Which pair of circles shown above are externally tangent?

b. Which pair are internally tangent?

Find the measure of central $\angle 1.$

The number of odd vertices will tell you whether or not a network can be traced without backtracking. Do you see how? If not, read on.

suppose that a given network can be traced without backtracking.

a. Consider a vertex that is neither the start nor end of a journey through this network. Is such a vertex odd or even?

b. Now consider the two vertices at the start and finish of a journey through this network. Can both of these vertices be odd? Even?

c. Can just one of the start and finish vertices be odd?

Find the measure of central $\angle 1.$

In exercises $2-7$ find the measure of the arc.

$\stackrel{⏜}{ABD}$

Plane Z passes through the center of sphere Q.

1. Explain why $QR=QS=QT$.
2. 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).