Central & Inscribed Angles

Dr. Tom Giles

An inscribed angle, (B), is an angle drawn inside of a circle such that...

• its vertex lies on the circumference of a circle and

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• its sides intercept the circle (A and C).

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​Inscribed Angles

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The Central Angle of a circle is an angle whose...

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• vertex is at the center (0) of a circle and...

• ​The two arms form two radii of the circle

• intersecting the arc of the circle at different points

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​Central Angle

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Note that the Central Angle (AOB) cuts the circle in two points...

• at Point A

• at point B

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​The Arc AB is called the...

Intercepted Arc

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Central Angle = Intercepted Arc​

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​Intercepted Arc, Central angle and Inscribed Angle

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Inscribed Angle = 1/2( Intercepted Arc )​

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The Central angle angle and the Inscribed Arc have the same measure​.

So, if the Central angle = 40^o

​The Intercepted Arc measure = 40^o

​Angle R = Arc AL

​Central Angles and Intercepted Arc Measure

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The Intercepted Arc is Twice the measure of the Inscribed Angle.

So, if the Inscribed angle = 20^o

​The Intercepted Arc measure = 40^o

​Angle C = 1/2 Arc AL

​Inscribed Angles and Intercepted Arc Measure

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