2. 外语
  3. In the figure above, points A, B, C, and D are collinear and are semicircles with diameters d1 cm, d2 cm, and d3 cm, respective

In the figure above, points A, B, C, and D are collinear and are semicircles with diameters d1 cm, d2 cm, and d3 cm, respective

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问题
In the figure above, points A, B, C, and D are collinear and are semicircles with diameters d1 cm, d2 cm, and d3 cm, respectively. What is the sum of the lengths of , in centimeters?
(1) d1:d2:d3 is 3:2:1.
(2) The length of AD is 48 cm.
选项 A、Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B、Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C、BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D、EACH statement ALONE is sufficient.
E、Statements (1) and (2) TOGETHER are NOT sufficient.
答案B
解析 Since the circumference of a semicircle is π(diameter/2), it follows that has length π(d1/2)cm, has length π(d2/2)cm, and has length π(d3/2) cm. Therefore, the sum of the lengths, in centimeters, of . is π(d1/2)+π(d2/2)+π(d3/2)=(π/2)(d1/2+d2/2+d3/2)
Determine the value of(π/2)(d1/2+d2/2+d3/2)
(1)     Given that d1：d2：d3 is 3:2:1, it is not possible to determine the value of (π/2)(d1/2+d2/2+d3/2) because d1, d2, and d3 could be 3,2, and 1 (d1 + d1 + d1 = 6) or d1, d1, and d1 could be 6, 4, and 2 (d1 + d2 + d3 = 12); NOT sufficient.
(2)     Given that AD = 48 and AD = d1 + d1 + d1, it follows that = (π/2)(d1/2+d2/2+d3/2)=(π/2)(48); SUFFICIENT.
The correct answer is B;
statement 2 alone is sufficient.
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