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![Page 1: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/1.jpg)
12.1 Tangent Lines Liedman
Tangent line: A line that intersects a circle once.
Point of tangency: The point where a circle and a tangent intersect. (T)
Ex:
90 + 90 + 152 + x = 360
332 + x = 360
X = 28
Ex: CB is tangent to Circle O. Find the value of x.
X = 180-90-26 = 64
Ex:
x² + 24² = (x+18)²
x² + 576 = x² + 36x + 324
252 = 36x
X = 7
![Page 2: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/2.jpg)
Ex: What is the value of x of Circle D?
x² + 12² = (x+8)²x² + 144 = x² + 16x + 6480 = 16xX = 5
Ex:
5² + 12² = 8²169 ≠ 64MN is not tangent since it is not perpendicular.
Ex: Circle O is inscribed in ΔABC. Find the perimeter of the ΔABC.
10 + 10 + 15+ 15 + 8 + 8 = 66 cm
7² + 24² = 25²49 + 576 = 625625 = 625MN is tangent since it is perpendicular.
![Page 3: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/3.jpg)
12.2 Chords and Arcs
Chord: A segment whose endpoints are on a circle
Ex: The circles are congruent. What can you conclude?
![Page 4: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/4.jpg)
Ex: What is the length of RS? Ex: What is x?
25 x = 16
![Page 5: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/5.jpg)
Ex: Find the missing variable.
3² + 7² = r² 11² + y ² = 15²
r = 7.6 y = 10.2
X = 1
![Page 6: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/6.jpg)
![Page 7: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/7.jpg)
12.3 Inscribed Angles
Inscribed angle: An angle whose vertex is on the circle and sides are chords.
Intercepted arc: An arc whose endpoints are the inscribed angle.
Ex: Find the missing angles.
50 a = 120 b= 75 m<A = 95, m<B = 77, m<C = 85, m<D = 103
Ex: Find the missing variables.
5x+110=180 x= 14 a = 180-68 = 112
104=2y= 180 y=38 b = 224 – 104 = 120
c = 142 – 104 = 38
![Page 8: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/8.jpg)
Ex: What is the m<A? 90º Ex: What is the measure of <2? 38º
43 x= 16 y = 14
Ex:
M<SQP = ½(212) = 106º
M<PQR = 74º
![Page 9: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/9.jpg)
12.4 Angle Measures and Segment Lengths
Ex: Find the value of the variables.
X = ½(112+140) x = ½(90-20)
X = 126 x = 35
20 = ½(95-z) 35 = ½(x + 30)
40 = 95 – z 70 = x + 30
Z = 55 x = 40
X = ½(240-120) m<1 = ½(170-55)
X = 60 m<1 = 57.5
![Page 10: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/10.jpg)
6.5m = 3(7) (20+14)14 = (x+16)16 (8+6)6 = (y+7)7 (16+8)8 = z²M = 3.2 x = 13.8 y = 5 z = 13.9
![Page 11: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/11.jpg)
12.5 Circles in the Coordinate Plane
Ex: What is the standard equation of a circle.
Center (-3, 5) Radius 6 Center: (6, 0) Radius:3
(x + 3)² + (y-5)² = 36 (x-6)² + y² = 9
Ex: What is the standard equation of the circle?
(x-2)² + (y-2)² = 16 x² + (y-3)² = 16
Ex: Find the center and radius of each circle. Then graph the circle.
x² + (y-2)² = 49 (x-4)² + (y + 3)² = 16
Center: (0,2) Center: (4,-3)
Radius: 7 Radius: 4
![Page 12: liedmanmath.weebly.com · Web viewCenter (-3, 5) Radius 6Center: (6, 0) Radius:3 (x + 3)² + (y-5)² = 36(x-6)² + y² = 9 Ex: What is the standard equation of the circle? (x-2)²](https://reader033.vdocuments.us/reader033/viewer/2022060823/609d0551a82b535055420c6f/html5/thumbnails/12.jpg)
Ex: Write the standard equation of the circle with the given center and passes through the given point.
Center: (-2,6) Point (-2, 10)
1.) Find the radius using the distance formula d=√(x1−x2)2+( y1− y2)
2
d = √ (−2— 2 )2+(6−10) ²=4
2. Write equation using radius and the center.
(x+ 2)² + (y – 6)² = 16
Center: (4,3) Point (-1,1)
1. Radius: √ (4−−1 )2+(3−1) ²=√29
2. (x-4)² + (y-3)² = 29