10.1 Angles in Circles

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Circle Geometry10.1 Exploring Angles in a Circle

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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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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