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Eight points are equally spaced on a circle.
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Updated on: 05 Jun 2019, 08:02
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Eight points are equally spaced on a circle. If 3 of the 8 points are to be selected at random, what is the probability that a triangle having the 3 points chosen as vertices will be a right triangle?
Eight points are equally spaced on a circle.
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05 Jun 2019, 13:02
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AparnaHarri wrote:
Eight points are equally spaced on a circle. If 3 of the 8 points are to be selected at random, what is the probability that a triangle having the 3 points chosen as vertices will be a right triangle?
A) 1/14 B) 1/7 C) 3/14 D) 3/7 E) 6/7
TOUGH question!!!
Key property: An inscribed angle that contains (aka "holds") the DIAMETER will be a 90-degree angle.
For example, let's draw one of the diameters...
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points1.png [ 4.98 KiB | Viewed 16340 times ]
The inscribed angle that contains (aka "holds") the DIAMETER will be a 90-degree angle.
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points2.png [ 6.04 KiB | Viewed 16085 times ]
Likewise, this inscribed angle also contains (aka "holds") the DIAMETER, so it will also be a 90-degree angle.
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points3.png [ 5.78 KiB | Viewed 16102 times ]
So, for the ONE PARTICULAR diameter (shown below)...
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points4.png [ 5.52 KiB | Viewed 16349 times ]
...we can see that, if we make any of the 6 points the 3rd vertex of the triangle, we will get a right triangle.
This means that, FOR EACH diameter in our circle, there are 6 points that will create a right triangle.
Since there are 4 diagonals altogether....
Attachment:
Eight points are equally spaced on a circle. If 3 of the 8 points5.png [ 6.35 KiB | Viewed 16471 times ]
....we know that the TOTAL number of right triangles possible = (4)(6) = 24
--------------------------------------- Now we need to determine how many different triangles can be created by selecting 3 of the 8 points. Since the order in which we select the 3 points does not matter, we can use COMBINATIONS. We can select 3 points from 8 points in 8C3 ways
8C3 = (8)(7)(6)/(3)(2)(1) = 56
----------------------------------------- So, P(we get a right triangle) = (total number of RIGHT triangles possible)/(total number of triangles possible) = 24/56 = 3/7
Re: Eight points are equally spaced on a circle.
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15 Apr 2020, 09:18
Expert Reply
Remember the difference between an official question, on which you should always rely your final call for the GRE exam, and a NON-official question is just in that: the non-official could be time-consuming and stop.
Official questions might be time-consuming BUT there is ALWAYS a shortcut to test your reasoning skills.
Schools: Copenhagen Business School - Class of 2022
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Re: Eight points are equally spaced on a circle.
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15 Apr 2020, 10:18
1
Completely agree with you carcass. I am trying to get in as many exercises as possible and, for some topics such as probability, I jump to non-official material or gmat, since there is not much official material. Otherwise ETS all the way haha Cheers!
Re: Eight points are equally spaced on a circle.
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29 Aug 2024, 08:11
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Re: Eight points are equally spaced on a circle. [#permalink]