chapter 10 : circles
DESCRIPTION
10.5.1 Apply Other Angle Relationships in Circles. Chapter 10 : Circles. If a chord intersects a tangent then the measure of the angle is one half the measure of the intercepted arc. Chord Tangent Intersect Theorem. m1= ½ mACB. C. A. m2= ½ mAB. 1. 2. B. - PowerPoint PPT PresentationTRANSCRIPT
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10.5.1 Apply Other Angle Relationships in Circles
![Page 2: Chapter 10 : Circles](https://reader036.vdocuments.mx/reader036/viewer/2022081501/56814be1550346895db8bb94/html5/thumbnails/2.jpg)
If a chord intersects a tangent then the measure of the angle is one half the measure of the intercepted arc
A
B
C
1 2
m1= ½ mACB
m2= ½ mAB
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The measure of each angle is one half the sum of the intercepted arcs
A
BC1
2
D
3
4
Since 1 2
m3 = m4 = ½ (mCA + mBD)
m1 = m2 = ½ (mCD + m AB)
![Page 4: Chapter 10 : Circles](https://reader036.vdocuments.mx/reader036/viewer/2022081501/56814be1550346895db8bb94/html5/thumbnails/4.jpg)
If an angle is outside the circle the measure of the circle is one half the difference of the intercepted arc 3 cases, same rule:
A
B
C
1D
A
C
1
A
B
C
1
B
m1 = ½ (mAB – mCD)
m1 = ½ (mABC – mCA)
m1 = ½ (mAC – mCB)
![Page 5: Chapter 10 : Circles](https://reader036.vdocuments.mx/reader036/viewer/2022081501/56814be1550346895db8bb94/html5/thumbnails/5.jpg)
A
B
C
D
E
F
60⁰
80⁰
40⁰
)(2
160 mABmACB
mABmACB 120
mABmACB 360
mACB*2480
mACB240
mAB120
)(2
180 mBCmCAB
mBCmCAB 160
mBCmCAB 360
mCAB*2520mCAB260
mBC100
)(2
140 mACmABC
mACmABC 80mACmABC 360
mABC*2440mABC220mAC140
![Page 6: Chapter 10 : Circles](https://reader036.vdocuments.mx/reader036/viewer/2022081501/56814be1550346895db8bb94/html5/thumbnails/6.jpg)
p. 683 1 – 6, 10 – 13, 16 - 20, 23 – 27odd, 32 -
38even