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Six points lie on a circle. How many quadrilaterals can be drawn joining these points?
- a)72
- b)36
- c)25
- d)15
- e)120
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Six points lie on a circle. How many quadrilaterals can be drawn joini...
The number of quadrilaterals that can be formed is 6C4 = (6 x 5 x 4 x 3)/(4 x 3 x 2) = 15.
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Six points lie on a circle. How many quadrilaterals can be drawn joini...
Solution:
To form a quadrilateral, we need to choose 4 points from 6 points.
The number of ways to choose 4 points from 6 is:
6C4 = (6*5)/(2*1) = 15
Therefore, there are 15 ways to choose 4 points from 6.
But, we need to consider that any 4 chosen points will form a quadrilateral only if they do not lie on a straight line.
Let us consider the cases where the 4 chosen points lie on a straight line.
Case 1: All 4 points lie on a diameter of the circle.
In this case, we can form only one quadrilateral, as there is only one way to choose 4 points on a diameter of the circle.
Case 2: Three points lie on a diameter of the circle.
In this case, we can form only one quadrilateral, as the fourth point can be chosen from the remaining 3 points, and only one of these combinations will not form a straight line.
Therefore, the total number of quadrilaterals that can be formed is:
15 - 2 = 13
Hence, the correct option is D) 15.
To form a quadrilateral, we need to choose 4 points from 6 points.
The number of ways to choose 4 points from 6 is:
6C4 = (6*5)/(2*1) = 15
Therefore, there are 15 ways to choose 4 points from 6.
But, we need to consider that any 4 chosen points will form a quadrilateral only if they do not lie on a straight line.
Let us consider the cases where the 4 chosen points lie on a straight line.
Case 1: All 4 points lie on a diameter of the circle.
In this case, we can form only one quadrilateral, as there is only one way to choose 4 points on a diameter of the circle.
Case 2: Three points lie on a diameter of the circle.
In this case, we can form only one quadrilateral, as the fourth point can be chosen from the remaining 3 points, and only one of these combinations will not form a straight line.
Therefore, the total number of quadrilaterals that can be formed is:
15 - 2 = 13
Hence, the correct option is D) 15.
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Six points lie on a circle. How many quadrilaterals can be drawn joining these points?a)72b)36c)25d)15e)120Correct answer is option 'D'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Six points lie on a circle. How many quadrilaterals can be drawn joining these points?a)72b)36c)25d)15e)120Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six points lie on a circle. How many quadrilaterals can be drawn joining these points?a)72b)36c)25d)15e)120Correct answer is option 'D'. Can you explain this answer?.
Six points lie on a circle. How many quadrilaterals can be drawn joining these points?a)72b)36c)25d)15e)120Correct answer is option 'D'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Six points lie on a circle. How many quadrilaterals can be drawn joining these points?a)72b)36c)25d)15e)120Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Six points lie on a circle. How many quadrilaterals can be drawn joining these points?a)72b)36c)25d)15e)120Correct answer is option 'D'. Can you explain this answer?.
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