chapter 10 : circles
Post on 16-Jan-2016
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10.5.1 Apply Other Angle Relationships in Circles
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
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)
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)
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
p. 683 1 – 6, 10 – 13, 16 - 20, 23 – 27odd, 32 -
38even
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