9-16 Arc, Arc, Arc..... Name __________________________________________
"Semi" is a prefix that means half, so a semi-circle is a half of a circle. In this handout we will learn some
of the uses of semi-circles.
1) We will be finding the center of a circle. I hope you remember the two ways to do this. One way is to
draw any chord. Then draw a segment perpendicular to the chord going through its midpoint.
Finally, find the midpoint of this diameter you just made. What is the other way?
2 a) Find the center of this circle and label it C and also label the diameter EO.
b) You have divided the circle in half, so you have made two semi-circles. Now let's learn how to
name them. Shade in either of the semi-circles. Why do you think we can not just call it semi-
c) Hopefully you noticed that there are two possible arcs that could share the name EO. That is why
we really need three points to name a semi-circle.
This semi-circle is namedarc EIO. Hey, maybe this
arc lives at Old McDonald's farm. (Get it?
know… an arc arc there and an arc arc here, there
arc, here an arc, everywhere an arc arc. EI EIO)
Actually, the symbol for the word arc is a little arc above
the letters like this.
There is one other way we can name this arc. What is it? ______________
3 a) We usually name arcs by their endpoints. Here are some examples:
The dark arc is called arc EO or arc OE. If you w anted to refer to
the other longer (lighter) arc , you w ould have to us e points
Its name is arc OIE or __________. Old McDonald is proud.
Minor arcs are "smaller" than semi-circ les, w hile the "larger" ones
are calledmajor arcs.
Name the following darkened arcs two different ways. Use the new symbol you learned.
b) c) d)
4 a) We will draw a running track. Here's what it will look like. Follow these steps to draw it. First use
your protractor and ruler to lightly draw a rectangle with a length of 41/4" and a width of 23/8".
Leave room on the ends to make the curves.
b) Find the midpoint of both vertical ends and mark them with a light point.
c) Make the curves on the end. Set your compass to half the width of the end. Then put the
compass on the midpoint you found and draw a semicircle on each end.
d) Now use your Algebra skills to find the length around the track if an ant was running in the outside
lane. (You will use a formula, so copy, fill in, and work as you go down the page.) The total length
will be the two straight-aways and the two semi-circles.
9-16 page 3 Arc, Arc, Arc..... Name __________________________________________
Example: Draw an arc w ith a 45° meas ure. 5) a) Draw an arc w ith a meas ure of 70°.
Firs t just draw a 45° angle.
Then just use the vertex of the angle
to draw a c ircle.
b) Label the arc XY and shade it darker.
The measure of arc AB is 45°.
6) Draw an arc with a measure of: (Shade the arcs a little darker.)
a) 90° b) 135°
c) 180° d) 270° (It can be done in a circle)
7) What is the measure of an arc that is the size of a complete circle? ______________8) Draw a 60° arc
in each of these circles and then shade each arc so it is darker than the circle.
Each of those arcs have the same measure, even though some may think the one on the left has a
larger measure just because of the length.
9) Divide this pie into 6 equal pieces. Label every angle you measure. From now on, you'll get to be in
charge of cutting the pies at your house.
10) Which arc do you believe has the largest measure? Why? ______________