Number of right angled triangles formed by vertices of a 14-gon
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Here's a question that I found on the website of International Kangaroo Maths Contest. The question goes like this:
What is the total number of right angled triangles that can be formed by joining the vertices of a regular 14-gon?
Correct Answer: The correct answer as given on the website is $84$.
What I did:
First of all, I calculated the total number off triangles (right angled or not) that can be formed by using the vertices of a regular 14-gon that is $^{14}C_3=364$.
However, I can't figure out how to count which ones of these $364$ triangles are right angled. Please help me in this regard.
Thanks for the attention!
combinatorics polygons
asked Nov 18 at 9:48
Faiq Irfan
540317
add a comment |
up vote
1
down vote
favorite
Here's a question that I found on the website of International Kangaroo Maths Contest. The question goes like this:
What is the total number of right angled triangles that can be formed by joining the vertices of a regular 14-gon?
Correct Answer: The correct answer as given on the website is $84$.
What I did:
First of all, I calculated the total number off triangles (right angled or not) that can be formed by using the vertices of a regular 14-gon that is $^{14}C_3=364$.
However, I can't figure out how to count which ones of these $364$ triangles are right angled. Please help me in this regard.
Thanks for the attention!
combinatorics polygons
asked Nov 18 at 9:48
Faiq Irfan
540317
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Here's a question that I found on the website of International Kangaroo Maths Contest. The question goes like this:
What is the total number of right angled triangles that can be formed by joining the vertices of a regular 14-gon?
Correct Answer: The correct answer as given on the website is $84$.
What I did:
First of all, I calculated the total number off triangles (right angled or not) that can be formed by using the vertices of a regular 14-gon that is $^{14}C_3=364$.
However, I can't figure out how to count which ones of these $364$ triangles are right angled. Please help me in this regard.
Thanks for the attention!
combinatorics polygons
asked Nov 18 at 9:48
Faiq Irfan
540317
Here's a question that I found on the website of International Kangaroo Maths Contest. The question goes like this:
What is the total number of right angled triangles that can be formed by joining the vertices of a regular 14-gon?
Correct Answer: The correct answer as given on the website is $84$.
What I did:
First of all, I calculated the total number off triangles (right angled or not) that can be formed by using the vertices of a regular 14-gon that is $^{14}C_3=364$.
However, I can't figure out how to count which ones of these $364$ triangles are right angled. Please help me in this regard.
Thanks for the attention!
combinatorics polygons
combinatorics polygons
asked Nov 18 at 9:48
Faiq Irfan
540317
asked Nov 18 at 9:48
Faiq Irfan
540317
asked Nov 18 at 9:48
Faiq Irfan
540317
asked Nov 18 at 9:48
Faiq Irfan
540317
asked Nov 18 at 9:48
Faiq Irfan
540317
540317
add a comment |
add a comment |
1 Answer
1
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4
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Remember that if two points of triangle are makeing diameter of circle circumscribed to this triangle than this one is right.
We have $7$ diameters and for each one we have 6 point on each side. So we have $$7cdot 12=84$$ right triangles.
answered Nov 18 at 9:51
greedoid
35.2k114489
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
accepted
Remember that if two points of triangle are makeing diameter of circle circumscribed to this triangle than this one is right.
We have $7$ diameters and for each one we have 6 point on each side. So we have $$7cdot 12=84$$ right triangles.
answered Nov 18 at 9:51
greedoid
35.2k114489
add a comment |
up vote
4
down vote
accepted
Remember that if two points of triangle are makeing diameter of circle circumscribed to this triangle than this one is right.
We have $7$ diameters and for each one we have 6 point on each side. So we have $$7cdot 12=84$$ right triangles.
answered Nov 18 at 9:51
greedoid
35.2k114489
add a comment |
up vote
4
down vote
accepted
up vote
4
down vote
accepted
Remember that if two points of triangle are makeing diameter of circle circumscribed to this triangle than this one is right.
We have $7$ diameters and for each one we have 6 point on each side. So we have $$7cdot 12=84$$ right triangles.
answered Nov 18 at 9:51
greedoid
35.2k114489
Remember that if two points of triangle are makeing diameter of circle circumscribed to this triangle than this one is right.
We have $7$ diameters and for each one we have 6 point on each side. So we have $$7cdot 12=84$$ right triangles.
answered Nov 18 at 9:51
greedoid
35.2k114489
answered Nov 18 at 9:51
greedoid
35.2k114489
answered Nov 18 at 9:51
greedoid
35.2k114489
answered Nov 18 at 9:51
greedoid
35.2k114489
35.2k114489
add a comment |
add a comment |
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