SAT Math Multiple Choice Question 718: Answer and Explanation

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Question: 718

13. Images

Note: Figure not drawn to scale.

The figure above shows two concentric circles with center O. If OD = 3, DB = 5, and the length of arc AB is 5π, what is the length of arc CD?

  • A. Images
  • B. Images
  • C. 3π
  • D. Images

Correct Answer: B

Explanation:

B

Special Topics (arcs) HARD

Images

First, we should make sure we mark up the diagram with the measurements we know: OD = 3 and DB = 5. This means that the radius of the small circle is 3 and the radius of the large circle is 8. Notice that sectors AOB and COD share a central angle, and therefore are similar. So the measures of arc CD and arc AB are

in a ratio of 3:8.

Images

Cross multiply:

Images

Divide by 8:

Images

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