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Eight points are equally spaced on a circle.
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Updated on: 05 Jun 2019, 08:02
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?
A) 1/14
B) 1/7
C) 3/14
D) 3/7
E) 6/7
A) 1/14
B) 1/7
C) 3/14
D) 3/7
E) 6/7
Originally posted by AparnaHarri on 31 May 2019, 00:58.
Last edited by Carcass on 05 Jun 2019, 08:02, edited 2 times in total.
Last edited by Carcass on 05 Jun 2019, 08:02, edited 2 times in total.
Edited the OA
Re: Eight points are equally spaced on a circle.
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31 May 2019, 01:48
31 May 2019, 01:48
Expert Reply
Please Sir,
follow the rules for posta on the board https://gre.myprepclub.com/forum/rules-for ... -1083.html.
The title of the question must be appropriate.
Moreover, provide the Official Answer.
Regards
follow the rules for posta on the board https://gre.myprepclub.com/forum/rules-for ... -1083.html.
The title of the question must be appropriate.
Moreover, provide the Official Answer.
Regards
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Eight points are equally spaced on a circle.
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05 Jun 2019, 13:02
05 Jun 2019, 13:02
4
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
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 16669 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 16407 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 16421 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 16680 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 16884 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
Answer: D
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