U7L1-2 Chords, Arcs, Central and Inscribed Angles

Chords, Arcs, Central and Inscribed Angle

By Maria Cruz Farooqi

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Diameters and ​

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are 2 types of ​

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that appear in circles. Here are some additional geometric objects associated with ​

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.

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A ​

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is a line segment whose endpoints are on the circle.

A ​

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in a circle is an angle whose vertex is at the center of the circle.

An ​

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is the portion of a circle between 2 points on the circle.

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chord

central angle

arc

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The measure of an arc is defined as the ​

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formed by the radii drawn to the ​

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.

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measure of the central angle

endpoints of the arc

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• center point

• circumference

• arc

• radius

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• arc

• circumference

• chord

• radius

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• center point

• circumference

• diameter

• chord

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• a diameter

• a central angle

• arc

• radius

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• an arc

• a diameter

• a central angle

• a radius

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• an arc

• a diameter

• a radius

• a central angle

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• a radius

• a central angle

• a diameter

• an arc

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We have discussed central angles such as angle ​

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. Another kind of angle in a circle is an inscribed angle, or an angle formed by 2 chords that ​

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. In the image, angle ​

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is an inscribed angle.

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It looks as though the inscribed angle is ​

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the central angle that defines the same arc. In fact, the measure of an inscribed angle is always ​

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of the associated central angle. For example, if the central angle AOB measures 50 degrees, the inscribed angle ACB must measure ​

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degrees. This also means that all inscribed angles that define the ​

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are congruent.

Multiple Choice

• 12

• 24

• 48

• 60

Multiple Choice

• A

• B

• C

• D

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Find the measure of arc BC

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Find the measure of arc BC

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Find m<B