guerrero wrote:If points A and B are randomly placed on the circumference of a circle with radius 2, what is the probability that the length of chord AB is greater than 2?
A)1/4
B)1/3
C)1/2
D)2/3
E)3/4
Question rephrased: Once A has been placed on the circle, what is the probability that B can be placed on the circle such that AB>2?
AB=2 if B is placed to the left or right of A as shown by B� and B₂ in the figure above.
If either B� or B₂ moves CLOSER to A, then AB<2.
Implication:
Since ∠B�OB₂ = 60+60 = 120º, and 120/360 = 1/3, AB≤2 for 1/3 of the circle.
Thus, AB>2 for the remaining 2/3 of the circle.
Resulting probability:
P(AB>2) = 2/3.
The correct answer is
D.
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