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0 votes
1 answer
788 views

How many obtuse angle triangles are possible in a regular Heptagon by joining its vertices?

I am only able to make one possible case, Where we take any 3-consecutive vertices, since one of the vertices contains angle of Heptagon, which is approximately 128.57°, we get 7 such triangles. I am ...
polaris inc.'s user avatar
2 votes
1 answer
393 views

Number of isoceles triangles formed by the vertices of a polygon that are not equilateral

QUESTION: Let $A_1,A_2,...,A_n$ be the vertices of a regular polygon with $n$ sides. How many of the triangles $△A_iA_jA_k,1 ≤ i < j < k ≤ n,$ are isosceles but not equilateral? MY APPROACH: ...
Stranger Forever's user avatar
23 votes
4 answers
93k views

How many triangles can be formed by the vertices of a regular polygon of $n$ sides?

How many triangles can be formed by the vertices of a regular polygon of $n$ sides? And how many if no side of the polygon is to be a side of any triangle ? I have no idea where I should start to ...
Bsonjin's user avatar
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