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We'll begin by arbitrarily placing point A somewhere on the circumference.BTGModeratorVI wrote: ↑Fri Apr 10, 2020 8:14 amIf 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
Answer: D
Source: Magoosh
Let O be the center of the circle. If we fix point A somewhere on the circumference of the circle, and if B is anywhere on the right or left of point A such that angle AOB is no greater than 60 degrees, then the length of chord AB will be no greater than 2. That is, since B can be to the right or left of point A, then B can be anywhere on a 60 + 60 = 120-degree arc (where A is the center of this arc) such that chord AB is no longer than 2. However, if B is anywhere outside this 120-degree arc (i.e., B is anywhere on the 240-degree arc that is outside of the 120-degree arc), then chord AB will be longer than 2. Since the circle has 360 degrees, the probability B is on the 240-degree arc is 240/360 = 2/3.BTGModeratorVI wrote: ↑Fri Apr 10, 2020 8:14 amIf 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
Answer: D
Source: Magoosh
