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Name: _________________________________________________________ Geometry Pd. ______ Circle Summary Sheet Topic Overview Big Ideas Center Radius Form, for circle centered at (h,k) with radius, r 12-1 (π₯ β β)2 + (π¦ β π)2 = π 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 xβs and yβs 3. Divide middle term by 2 and square it β ADD TO BOTH SIDES! 4. put factors into Squared Form ο ( )2 ( remember the number will be half of the middle term) 5. Youβre in center-radius form!!! ο We complete the square twice to put general form equations of circles into Center-Radius form, then graph! ο Recognize a circle by finding an π₯ 2 12-4 Systems with Circles Any point of intersection is a solution to the system β solve graphically! 12-5 Systems with Parabolas Any point of intersection is a solution to the system β 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 πππππ ππππ π’ππ ππ π πππ‘ππ π΄πππ ππ π ππππ‘ππ = π΄πππ ππ π πΆπππππ ( ) 360 12-7 Area of a circle = ππ 2 12-8 Arc Length of a Sector (In degrees) πππππ ππππ π’ππ ππ π πππ‘ππ π΄ππ πΏππππ‘β = πΆππππ’ππππππππ ( ) 360 Circumference of a circle = ππ 12-9 Solving for arc length IN RADIANS s = rπ where: s = arc length; r = radius; π = central angle Radians β 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 = Ο 180 Station 1: Circle Equations 1. Write the equation of a circle with a radius of β5 units and a center (3,-2). 2. Identify the center and radius of the following circle. Leave answers in simplest radical form. π₯ 2 + (π¦ + 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 β 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: 7π₯ 2 + 7π¦ 2 = 448 7. Graph the following circle: x2 β 2x + y2 + 8y β 8 = 0 Station 2: Systems 1. Solve the following System of equations graphically: y = x2 +2x β 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. (π₯ β 4)2 + (π¦ + 2)2 = 9 π¦=1 4. Solve the following system of equations. State all solutions. 2π₯ 2 + 2π¦ 2 = 2 π₯ 2 + (π¦ β 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 π¦π2 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! Itβs 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 β 5 Start at station 2 #6 Start at Station 3 #7-9 Start at station 4 This is really difficult for me