SAT Math Multiple Choice Practice Question 589: Answer and Explanation

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Question: 589

3.

In the figure above, ACDF is a rectangle and the circle with center O has a radius of r. is tangent to the circle at point B, is tangent to the circle at point E, and COE measures 120°. If (not shown) passes through O, then what is the length of in terms of r ?

A. 2πr
B. 2r
C. 2r
D. 4πr
E. 4r

Correct Answer: E

Explanation:

E The phrase in terms of means that this is a Plugging In question. The figure above the question is not drawn to scale, so redraw or add to the figure based on information in the question. Because and are tangent to the circle, they form a 90° angle with a radius or diameter of the circle. Draw in diameter and mark the right angles. Draw the diagonal of the rectangle . The question states that ∠COE = 120° so ∠COB = 60°. We have a 30-60-90 triangle, COB, in which is the radius of the circle and the shortest side of the triangle. Time to plug in! If r = 5, the sides of this special right triangle are 5 : 5 : 10. So CO = 10, which is half the length of CF, which must equal 20. Now plug in r = 5 in the answers: A results in 10π; B results in 10; C gives 10; D gives 20π. Only E has a result of 20.

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