G CC-18 Circles
Activity 1
If 2 figures are similar then they have the same shape
and are proportional. In other words, one figure can be
mapped onto the other figure by using a scale factor.
Circle G has center (3, 4) and a radius of ______.
Circle H has center (8, 5) and radius of _____________.
1. Are the 2 circles the same
shape?__________________ Same size? ________________
2. How would you move circle G so that its center is mapped onto the center of circle H?
__________________________________________________
3. What is the scale factor you would use to make circle G the same size as circle H?
_______________________________________________
4. Find the following ratios:
a. Radius of circle G to circle H ________________________
b. Circumference of circle G to circle H __________________________________
5. Based on your findings above, are the 2 circles similar? Explain.
If 2 circles have radii of 4 and 5, are they similar? Explain.
If 2 circles have radii of ½ and 6, are they similar? Explain.
What can you conclude?
Activity 2
Prove that the length of the arc intercepted by a central angle of a
circle is proportional to the radius of the circle
Two concentric circles are shown. Radius: a __________ b ___________
Arc length: a _____________________ b _____________________
Find the length ( see page
Show
𝐴𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝑎
𝑟𝑎𝑑𝑖𝑢𝑠 𝑎
=
𝐴𝑟𝑐 𝑙𝑒𝑛𝑔𝑡ℎ 𝑏
𝑟𝑎𝑑𝑖𝑢𝑠 𝑏
) of arc s1 and s2.
Prove the relationship holds true for the 2 circles shown in this
diagram.
Activity 4: Radians and Degrees
Complete the table.
Activity 5: Converting measurements
Convert 10° to radians.
Conversion Factors ________________and_________________
Convert 100𝜋 to degrees.
Convert each measurement to radians. Show your work.
Convert each measurement
to degrees.
Show your work.