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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?
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