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If points A and B are randomly placed on the circumference of a circle

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If points A and B are randomly placed on the circumference of a circle [#permalink]

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New post 27 Oct 2010, 17:47
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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?

1/4
1/3
1/2
2/3
3/4
[Reveal] Spoiler: OA

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Re: If points A and B are randomly placed on the circumference of a circle [#permalink]

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New post 27 Oct 2010, 18:37
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Look at the figure. Let A be the first point which can be anywhere... Now AB and AC are chords of length 2 cm each giving you equilateral triangles BOA and COA. (Center of the circle is the point O)
If your second point is anywhere on arc BAC, the length of the chord will be less than or equal to 2. Else, it will be greater than 2.
Since the arc BAC subtends 120 degrees at the center, probability of chord length less than 2 cm is 1/3 and greater than 2 cm is 2/3
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Re: If points A and B are randomly placed on the circumference of a circle [#permalink]

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New post 01 Oct 2017, 04:20
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Re: If points A and B are randomly placed on the circumference of a circle   [#permalink] 01 Oct 2017, 04:20
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