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Question 15 of 18

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M:N:MC:14

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SAT

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Additional Topics in Math

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The figure presents a semicircle with a horizontal diameter labeled A B and a horizontal line segment labeled C D intersecting the semicircle at points C and D.

The semicircle above has a radius of r inches, and chord stack C D with bar on top is parallel to the diameter stack A B with bar on top. If the length of stack C D with bar on top is 2 over 3 of the length of stack A B with bar on top comma what is the distance between the chord and the diameter in terms of r?

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1 third straight pi r

Correct Answer: 
No

2 over 3 straight pi r

Correct Answer: 
No

fraction numerator square root of 2 over denominator 2 end fraction r

Correct Answer: 
No

fraction numerator square root of 5 over denominator 3 end fraction r

Correct Answer: 
Yes

Choice D is correct. This represents the length of the distance between the chord and the diameter, using a radius of the circle to create a triangle, and then the Pythagorean theorem to solve correctly: r squared equals x squared plus open parentheses 2 over 3 r close parentheses squared comma where r represents the radius of the circle and x represents the distance between the chord and the diameter.

Choice A is not the correct answer. It does not represent the length of the distance between the chord and the diameter. The student who selects this answer may have tried to use the circumference formula to determine the distance rather than making use of the radius of the circle to create a triangle.

Choice B is not the correct answer. It does not represent the length of the distance between the chord and the diameter. The student who selects this answer may have tried to use the circumference formula to determine the distance rather than making use of the radius of the circle to create a triangle.

Choice C is not the correct answer. It does not represent the length of the distance between the chord and the diameter. The student who selects this answer may have made a triangle within the circle, using a radius to connect the chord and the diameter, but then may have mistaken the triangle for a 45-45-90 triangle and tried to use this relationship to determine the distance.

Question Difficulty: 
hard
Objective: 

Students must make use of properties of circles and parallel lines in an abstract setting.