SAT Math Multiple Choice Question 980: Answer and Explanation

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Question: 980

In the figure above, circle O has a circumference of 12π. If AB = 8, what is BC

  • A.
  • B.
  • C.
  • D.

Correct Answer: B



Difficulty: Hard

Category: Additional Topics in Math / Geometry

Strategic Advice: Identify pieces of the figure that play roles in multiple shapes present (for example, a radius of the circle that is also a leg of a triangle), and transfer information as you work toward the answer.

Getting to the Answer: The circumference of circle O is 12π, so its radius must be 6(C = 2πr). You now know the lengths of two sides of ΔAOB (the given hypotenuse and the leg represented by the radius), and because it's a right triangle, you can use the Pythagorean theorem to find the length of the missing side (OB):

Don't stop yet; the question asks for BC, not OB. BC is equal to 6 - 2 , which is (because is also a radius). Factor out a 2 to get, which matches (B).

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