GRE Math : How to find the length of a chord

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : Geometry

Circlechord0

O is the center of the circle above.

The length of  is .

Quantity A: The area of the circle.

Quantity B: 

Which of the following is true?

Possible Answers:

The two quantities are equal.

Quantity B is greater.

Quantity A is greater.

The relationship cannot be determined.

Correct answer:

Quantity A is greater.

Explanation:

Circlechord0

O is the center of the circle above.

 The length of  is .

Quantity A: The area of the circle.

Quantity B: 

Do not be tricked by this question. It is true that  can be split into halves, each of which are  in length. These halves are not, however, radii to the circle. Since this does not go through the center of the circle, its length is shorter than the diameter. This means that the radius of the circle must be greater than . Now, if it were , the area would be . Since it is larger than , the area must be larger than . Quantity A is larger than quantity B.

Example Question #2 : Geometry

Circlechord1

O is the center of the circle above.

The circumference of the circle above is .

Quantity A: The length of .

Quantity B: 

Which of the following is true?

Possible Answers:

The two quantities are equal.

Quantity B is larger.

The relationship cannot be determined.

Quantity A is larger.

Correct answer:

Quantity B is larger.

Explanation:

Now, we know that the circumference of a circle is:

 or 

This means that the diameter of our circle is must be . Given this, we know that the  must be shorter than , for the diameter is the longer than any chord that does not pass through the center of the circle. Quantity B is larger than quantity A.

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