Download Name: Unit 12 Review Geometry Pd. ______ Date: ______ Circle

Name: _________________________________________________________
Geometry Pd. ______
Circle Summary Sheet
Topic Overview
Big Ideas
Center Radius Form, for circle centered at (h,k) with radius, r
12-1
(𝑥 − ℎ)2 + (𝑦 − 𝑘)2 = 𝑟 2
12-2
12-3
Unit 12 Review
Date: __________
Completing the square for center-radius form
1. Move loose numbers to one side
2. Group x’s and y’s
3. Divide middle term by 2 and square it – ADD TO BOTH SIDES!
4. put factors into Squared Form  ( )2 ( remember the number will be half of the middle term)
5. You’re in center-radius form!!!
 We complete the square twice to put general form equations of circles into Center-Radius form,
then graph!
 Recognize a circle by finding an 𝑥 2
12-4
Systems with Circles
Any point of intersection is a solution to the system – solve graphically!
12-5
Systems with Parabolas
Any point of intersection is a solution to the system – solve graphically!
Watch out for sneaky turning points and sneaky solutions- know how to manipulate your calculator!
( 12-6 was a quiz!)
Area of a Sector
𝑎𝑛𝑔𝑙𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑆𝑒𝑐𝑡𝑜𝑟 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝐶𝑖𝑟𝑐𝑙𝑒 (
)
360
12-7
Area of a circle = 𝜋𝑟 2
12-8
Arc Length of a Sector (In degrees)
𝑎𝑛𝑔𝑙𝑒 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑠𝑒𝑐𝑡𝑜𝑟
𝐴𝑟𝑐 𝐿𝑒𝑛𝑔𝑡ℎ = 𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 (
)
360
Circumference of a circle = 𝜋𝑑
12-9
Solving for arc length IN RADIANS
s = r𝜃
where: s = arc length; r = radius; 𝜃 = central angle
Radians – unit of angle measure
An angle is 1 radian when the length of the arc of the circle is equal to the radius
12-10
Conversions
Set up a proportion and solve for desired angle measure!
radians
degrees
=
π
180
Station 1: Circle Equations
1. Write the equation of a circle with a radius of √5 units and a center (3,-2).
2. Identify the center and radius of the following circle. Leave answers in simplest radical form.
𝑥 2 + (𝑦 + 5)2 = 50
3. Use the following equation for parts a-c
a) Write the equation in center-radius form
b) Identify the center and radius of the circle
center: __________ radius: ___________
c) Graph the circle →
4. Write the equation of the circle graphed below:
5. Write the equation of a circle whose center is (2,1) and passes through the point (2,-3)
6. Graph the following circle: 7𝑥 2 + 7𝑦 2 = 448
7. Graph the following circle:
x2 – 2x + y2 + 8y – 8 = 0
Station 2: Systems
1. Solve the following System of equations graphically:
y = x2 +2x – 3
y+x=1
2. How many solutions does this system have?
y = x2 - x - 6
y = 2x -8
What quadrant does the solution (s) fall in?
3. Solve the following system of equations. State all solutions.
(𝑥 − 4)2 + (𝑦 + 2)2 = 9
𝑦=1
4. Solve the following system of equations. State all solutions.
2𝑥 2 + 2𝑦 2 = 2
𝑥 2 + (𝑦 − 3)2 = 4
Station 3: Area of a Sector
1. Segment NM is 3.5 in. Find the area of the shaded region to the nearest whole number
2. The radius of the circle shown below is 8 in. Find the area of the shaded region to the nearest whole
number:
3. The area of sector FHE is 156.38 𝑦𝑑2
Round to the nearest tenth.
Station 4: Arc Length in degrees and/or radians
Convert the following:
1.
300° = _____________ radians
2.
________________ degrees = 12
𝜋
3. a) The length of minor arc SQ is 3.82 in. Find the circumference of circle R to the nearest inch.
b) What is the radius of circle R to the nearest tenth?( use your final answer from part A)
4) A central angle of a circular garden measures 2.5 radians and intercepts an arc of 20 feet. What is the radius
of the garden?
1) 8 ft
2) 50 ft
3) 100 ft
4) 125 ft
5) In a circle, a central angle intercepts an arc of 12 centimeters. If the radius of the circle is 6
centimeters, find the number of radians in the measure of the central angle.
6) In a circle whose radius is 10 ft., what is the length of the arc intercepted by a central angle of 4
radians
7) The accompanying diagram shows the path of a cart traveling on a circular track of radius 2.40
meters. The cart starts at point A and stops at point B, moving in a counterclockwise direction. What is
the length of minor arc AB, over which the cart traveled, to the nearest tenth of a meter?
Self-Assess for Success!
Fill in the following chart for each topic by placing a
check mark in the box that describes your knowledge of each
topic.
** Be honest! It’s just you looking at this! **
Topic
This is easy
for me
This is o.k.
for me
1. Graphing Circles
2. Writing Circle
Equations
3. Completing the
square to get equation
of circle in centerradius form
4. Graphing Parabolas
5. Solving Systems
Graphically
6. Area of a Sector
7. Arc Length Given
Degrees
8. Arc Length Given
Radians
9. Converting degrees
to radians
#1-3
Start at
station 1
#4 – 5
Start at
station 2
#6
Start at
Station 3
#7-9
Start at
station 4
This is
really
difficult for
me