central angle
DESCRIPTION
CENTRAL ANGLE. C. A. B. C. Answer: . A. B. D. C. A. B. By Construction:. Draw a circle with centre C. Draw radii AC and BC. Measure the angle formed. What is the measure of angle ACB? What is the measure of arc AB? Draw chords AD and BC. Measure ADB. What is m. - PowerPoint PPT PresentationTRANSCRIPT
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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