单选题
In the figure above, the radius of circle O is 3, and m∠AOB=60. What is the perimeter of the shaded region?
In the figure above, the radius of circle O is 3, and m∠AOB=60. What is the perimeter of the shaded region?
【正确答案】
C
【答案解析】Since each radius is 3, OA = OB, and by KEY FACT J3 m∠A = m∠B.
[*]
Then, 60 + x + x = 180 [*] x = 60. Therefore ΔAOB is equilateral, and AB = 3. The length of arc AB is [*] of the circumference. C = 2π(3) = 6π, so the length of arc AB = π. The perimeter of the region, then, is 3 + π.
**Use TACTIC 2, Chapter 10: trust the diagram. AB looks about the same as OB, so assume it is 3, and arc AB is clearly slightly bigger. Hence, the perimeter is a little more than 6. Choices A and B are both less than 5, which is definitely too small. Between C and D guess. C, 3 + re, is the better guess, because AB might be exactly 3.
[*]
Then, 60 + x + x = 180 [*] x = 60. Therefore ΔAOB is equilateral, and AB = 3. The length of arc AB is [*] of the circumference. C = 2π(3) = 6π, so the length of arc AB = π. The perimeter of the region, then, is 3 + π.
**Use TACTIC 2, Chapter 10: trust the diagram. AB looks about the same as OB, so assume it is 3, and arc AB is clearly slightly bigger. Hence, the perimeter is a little more than 6. Choices A and B are both less than 5, which is definitely too small. Between C and D guess. C, 3 + re, is the better guess, because AB might be exactly 3.