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10.1 Angles in Circles 1 March 24, 2014 Circle Geometry 10.1 Exploring Angles in a Circle
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10.1 Angles in Circles
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Circle Geometry10.1 Exploring Angles in a Circle
10.1 Angles in Circles
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Anatomy of a Circle
What do we know about a circle?
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Anatomy of a Circle
Chord: A line segment with both endpoints on a circle
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Anatomy of a Circle
Central Angle: An angle formed by two radii of a circle.
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Anatomy of a Circle
Inscribed Angle: An angle formed by two chords that share a common endpoint
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Anatomy of a Circle
Arc (of a circle): A portion of the circumference
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Properties of Angles
The inscribed angles subtended by the same arc are congruent.
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Tips and Tricks
If you see a bow tie, you have sets of inscribed angles.
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Properties of Angles
The measure of the central angle is equal to twice the measure of the inscribed angle subtended by the same arc.
B
A
C
O
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Tips and Tricks
If you see a Star Trek insignia, you have a set of inscribed angles and central angles.
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ExampleFind ∠ACD and ∠AOD if ∠ABD is 35˚
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ExampleFind ∠ACD and ∠AOD if ∠ABD is 35˚
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Properties of Angles
Angles inscribed in a semicircle are right angles.
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ExamplePoint C is the centre of the circle. The diameter AB is 10cm and the chord BD is 6 cm. B
D
C
A
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Example
Determine the measure of the missing angle
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Example
Determine the measure of angle y
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10.1 Angles in Circles
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Example
Determine the measure of the missing angles
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Example
Determine the measure of the missing angles
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Example
Determine the measure of the missing angle
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Questions page 3823, 4, 10, 12, 20a
