Intermediate Geometry : Plane Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #21 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is  and the measurement of the central angle is  degrees.

Possible Answers:

Correct answer:

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

Substitute in the given values for the central angle and the radius.

Solve.

Example Question #22 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is  and the measurement of the central angle is  degrees.

Possible Answers:

Correct answer:

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

Substitute in the given values for the central angle and the radius.

Solve.

Example Question #23 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is  and the measurement of the central angle is  degrees.

Possible Answers:

Correct answer:

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

Substitute in the given values for the central angle and the radius.

Solve.

Example Question #24 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is  and the measurement of the central angle is  degrees.

Possible Answers:

Correct answer:

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

Substitute in the given values for the central angle and the radius.

Solve.

Example Question #25 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is  and the measurement of the central angle is  degrees.

Possible Answers:

Correct answer:

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

Substitute in the given values for the central angle and the radius.

Solve.

Example Question #26 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is  and the measurement of the central angle is  degrees.

Possible Answers:

Correct answer:

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

Substitute in the given values for the central angle and the radius.

Solve.

Example Question #27 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is  and the measurement of the central angle is  degrees.

Possible Answers:

Correct answer:

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

Substitute in the given values for the central angle and the radius.

Solve.

Example Question #28 : How To Find The Length Of An Arc

Find the length of an arc if the radius of the circle is  and the measurement of the central angle is  degrees.

Possible Answers:

Correct answer:

Explanation:

An arc is just a piece—or a fraction—of a circle's circumference. Use the following formula to find the length of an arc:

Substitute in the given values for the central angle and the radius.

Solve.

Example Question #29 : How To Find The Length Of An Arc

In the figure below,. If  is  degrees, in degrees, what is the measure of ?

1

Possible Answers:

The measurement of  cannot be determined with the information given.

Correct answer:

Explanation:

Recall that when chords are parallel, the arcs that are intercepted are congruent. Thus, .

Then,  must also be  degrees.

Example Question #1 : How To Find The Angle Of A Sector

Circle

In the circle above, the length of arc BC is 100 degrees, and the segment AC is a diameter. What is the measure of angle ADB in degrees?

Possible Answers:

100

40

90

80

cannot be determined

Correct answer:

40

Explanation:

Since we know that segment AC is a diameter, this means that the length of the arc ABC must be 180 degrees. This means that the length of the arc AB must be 80 degrees. 

Since angle ADB is an inscribed angle, its measure is equal to half of the measure of the angle of the arc that it intercepts. This means that the measure of the angle is half of 80 degrees, or 40 degrees.

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