CENTRAL ANGLE
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Transcript of CENTRAL ANGLE
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CENTRAL ANGLE
A
B
C
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AB
C Answer:
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A
B
C
D
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By Construction:1. Draw a circle with centre C.2. Draw radii AC and BC.3. Measure the angle formed.
• What is the measure of angle ACB?• What is the measure of arc AB?
4. Draw chords AD and BC.5. Measure ADB.
– What is m
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A
B
C
D
INSCRIBED ANGLE
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An angle whose vertex is on the circle and whose sides are chords of the
circle.
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INSCRIBED ANGLE THEOREM
The measure of an inscribed angle is half the measure of
its intercepted arc.
PROOF
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Cases:
Case 1Case 2Case 3
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Cases:
Case 1Case 2Case 3
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Cases:
Case 1Case 2Case 3
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Cases:
Case 1Case 2Case 3
EXAMPLE
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Case 1:
1.
A
C
O
B
PROVED
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Case 2:
= =
=
A C
O
B
DPROVE
D
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Case 3:
1. =
2. • • • • =
A
C
O
B
D PROVED
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Example:
A
B
CD
In the accompanying figure, mAB=112, mBC=54, and mCD=88. Find m3.
SOLUTION
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Solution:mAB + mBC + mCD + mDA = 360 = =27°m2 = mDA = = 53°m3= m 1 + m2 = 27 + 53 = 80° EXERCISE
S
112 + 54 + 88 + mDA = 360mDA = 360m= mBC
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Exercises:
1. In O, AC is a diameter, mAD= 70, and m BDC = 30°. Determine the measures of the following:
a. Bb. Cc. BCd. ABe. ADBf. ADC
O
D A
CB
HOMEWORK
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Homework:
Given: Quadrilateral ABCD is a rectangle.
Prove: AC and BD are diameters of the circle.
A B
D C
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C
DONE
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A
B
C
DONE
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A
B
C
D
DONE