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  3. For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities

For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities

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问题 For each of Questions 1 to 9, compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the following four answer choices and fill in the corresponding oval to the right of the question.
(A)Quantity A is greater.
(B)Quantity B is greater.
(C)The two quantities are equal.
(D)The relationship cannot be determined from the information given.
A symbol that appears more than once in a question has the same meaning throughout the question.

选项
答案B
解析 In this question you are asked to compare x with 5, where x is the length of a line segment from the center of the circle to a point inside the circle. In a circle the easiest line segments to deal with are the radius and the diameter. Looking at the figure in the question, you can see that you can draw two radii, each of which "completes" a right triangle, as shown in the figure below.

    Since in one of the triangles the lengths of both legs are known, you can use that triangle to determine the length of the radius of the circle. The triangle has legs of length 3 and 4. If the length of the radius is r, then, using the Pythagorean theorem, you can see that
r2 = 32+ 42 or
r2 = 9+ 16 or
r2 = 25, and thus, r = 5
Since the length of the radius of the circle is 5 and the line segment of length x is clearly shorter than the radius, you know that x < 5, and the correct answer is Choice B.
    You could also see that the two triangles are congruent, and so x = 4, again yielding Choice B.
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