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In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon is
- a)20
- b)28
- c)8
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a polygon no three diagonals are concurrent. If the total number of...
A combination of four vertices is equivalent to one interior poin of intersection of diagonals.
∴ No. of interior points of intersection
⇒ nC4 = 70
⇒ n (n – 1) (n – 2) (n – 3) = 5. 6. 7. 8
∴ n = 8
So, number of diagonals = 8C2 – 8 = 20
∴ No. of interior points of intersection
⇒ nC4 = 70
⇒ n (n – 1) (n – 2) (n – 3) = 5. 6. 7. 8
∴ n = 8
So, number of diagonals = 8C2 – 8 = 20
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In a polygon no three diagonals are concurrent. If the total number of...
Explanation:
Given, in a polygon no three diagonals are concurrent and the total number of points of intersection of diagonals interior to the polygon is 70.
Let the polygon have n sides.
Number of ways to choose two vertices of a polygon = nC2
Number of diagonals in a polygon = nC2 - n
Given that no three diagonals are concurrent, the number of intersection points of diagonals interior to the polygon = nC4
Therefore, nC4 = 70
Solving this equation, we get n = 8
Number of diagonals in a polygon with n sides = nC2 - n = 8C2 - 8 = 20
Therefore, the number of diagonals of the polygon is option 'A', i.e., 20.
Given, in a polygon no three diagonals are concurrent and the total number of points of intersection of diagonals interior to the polygon is 70.
Let the polygon have n sides.
Number of ways to choose two vertices of a polygon = nC2
Number of diagonals in a polygon = nC2 - n
Given that no three diagonals are concurrent, the number of intersection points of diagonals interior to the polygon = nC4
Therefore, nC4 = 70
Solving this equation, we get n = 8
Number of diagonals in a polygon with n sides = nC2 - n = 8C2 - 8 = 20
Therefore, the number of diagonals of the polygon is option 'A', i.e., 20.
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In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon isa)20b)28c)8d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon isa)20b)28c)8d)None of theseCorrect answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon isa)20b)28c)8d)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a polygon no three diagonals are concurrent. If the total number of points of intersection of diagonals interior to the polygon be 70 then the number of diagonals of the polygon isa)20b)28c)8d)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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