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Twelve points are spaced evenly around a circle, lettered fr

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cbdscolin
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Twelve points are spaced evenly around a circle, lettered fr [#permalink] New post   Updated on: 18 Aug 2020, 16:10
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Twelve points are spaced evenly around a circle, lettered from A to L. Let N be the total number of isosceles triangles, including equilateral triangles, that can be constructed from three of these points. A different orientation of the same lengths counts as a different triangle, because a different combination of points form the vertices. What is the value of N?


A. 48

B. 52

C. 60

D. 72

E. 120
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B

Originally posted by cbdscolin on 16 Mar 2019, 21:25.
Last edited by Carcass on 18 Aug 2020, 16:10, edited 2 times in total.
Edited by Carcass
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Carcass
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Re: Number of Triangles [#permalink] New post   17 Mar 2019, 01:29
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There are 12 points at EQUAL interval..
So the isosceles triangle can have EQUAL sides of length.
Let's work on the central vertex.

A as the vertex between EQUAL sides..
The EQUAL sides can be 1 unit, two unit, 3 unit, 4 unit or 5 unit...
6 unit will be the diameter so not possible.
So A as central vertex can make 5 isosceles triangles.

Thus 12 vertices from A to L can make 12*5=60 such isosceles triangles.

However 4 units results in an equilateral triangle.
So we are counting the same triangle THREE times.
So actual different triangles with 4 unit as length = 12/3=4..
So we have 12-4=8 extra triangles counted..

Total = 60-8=52...

B
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Re: Number of Triangles [#permalink] New post   02 Sep 2019, 10:05
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I don't get the explanation. Can you please include graphs?
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Twelve points are spaced evenly around a circle, lettered fr [#permalink] New post   26 Apr 2020, 12:23
Twelve points are spaced evenly around a circle, lettered from A to L. Let N be the total number of isosceles triangles, including equilateral triangles, that can be constructed from three of these points. A different orientation of the same lengths counts as a different triangle, because a different combination of points form the vertices. What is the value of N?

A. 48
B. 52
C. 60
D. 72
E. 120
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Carcass
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Re: Number of Triangles [#permalink] New post   26 Apr 2020, 14:50
Expert Reply
Image

refer to this topic https://gmatclub.com/forum/twelve-point ... l#p1812685

Regards
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Twelve points are spaced evenly around a circle, lettered fr [#permalink] New post   22 Jul 2021, 10:07
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[quote="Carcass"]There are 12 points at EQUAL interval..
So the isosceles triangle can have EQUAL sides of length.
Let's work on the central vertex.

A as the vertex between EQUAL sides..
The EQUAL sides can be 1 unit, two unit, 3 unit, 4 unit or 5 unit...
6 unit will be the diameter so not possible.
So A as central vertex can make 5 isosceles triangles.

Thus 12 vertices from A to L can make 12*5=60 such isosceles triangles.

However 4 units results in an equilateral triangle.
So we are counting the same triangle THREE times.
So actual different triangles with 4 unit as length = 12/3=4..
So we have 12-4=8 extra triangles counted..


hello expert please explain
"However 4 units results in an equilateral triangle.
So we are counting the same triangle THREE times.
So actual different triangles with 4 unit as length = 12/3=4..
So we have 12-4=8 extra triangles counted "
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volcanictempest78
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Re: Twelve points are spaced evenly around a circle, lettered fr [#permalink] New post   13 Mar 2022, 21:40
Carcass wrote:
There are 12 points at EQUAL interval..
So the isosceles triangle can have EQUAL sides of length.
Let's work on the central vertex.

A as the vertex between EQUAL sides..
The EQUAL sides can be 1 unit, two unit, 3 unit, 4 unit or 5 unit...
6 unit will be the diameter so not possible.
So A as central vertex can make 5 isosceles triangles.

Thus 12 vertices from A to L can make 12*5=60 such isosceles triangles.

However 4 units results in an equilateral triangle.
So we are counting the same triangle THREE times.
So actual different triangles with 4 unit as length = 12/3=4..
So we have 12-4=8 extra triangles counted..

Total = 60-8=52...

B


I might be missing something but how does when know that a unit 4 will create a equilateral triangle
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SivhHarish
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Re: Twelve points are spaced evenly around a circle, lettered fr [#permalink] New post   29 Apr 2022, 00:36
Carcass wrote:
There are 12 points at EQUAL interval..
So the isosceles triangle can have EQUAL sides of length.
Let's work on the central vertex.

A as the vertex between EQUAL sides..
The EQUAL sides can be 1 unit, two unit, 3 unit, 4 unit or 5 unit...
6 unit will be the diameter so not possible.
So A as central vertex can make 5 isosceles triangles.

Thus 12 vertices from A to L can make 12*5=60 such isosceles triangles.

However 4 units results in an equilateral triangle.
So we are counting the same triangle THREE times.
So actual different triangles with 4 unit as length = 12/3=4..
So we have 12-4=8 extra triangles counted..

Total = 60-8=52...

B


I don't even understand this solution. Please a detailed explanation would be good.
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Re: Twelve points are spaced evenly around a circle, lettered fr [#permalink] New post   29 Apr 2022, 00:47
Expert Reply
The solution provided above is from a quant moderator on Gmat Club

The image also is another explanation provided by an expert.

Will see if GreenLight will step in. I do no not know how to help more sir

I am sorry
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Re: Twelve points are spaced evenly around a circle, lettered fr [#permalink] New post   14 Jun 2023, 23:56
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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