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8 points are marked on the circumference of a circle. The number of chords obtained by joining these in pairs is
- a)25
- b)27
- c)28
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
8 points are marked on the circumference of a circle. The number of ch...
This is an example of application of Permutation & combination in Geometry.
We need two points on the circumference of a circle to draw a chord.
Since 8 points are there, the problem reduces to finding number of ways 2 points can be selected out of 8 points.
=> C(8,2) = 8!/(2! 6!) = 8 x 7/2 = 28 chords
Most Upvoted Answer
8 points are marked on the circumference of a circle. The number of ch...
Given: 8 points marked on the circumference of a circle
To find: the number of chords obtained by joining these in pairs
Solution:
Number of chords that can be formed between n points on a circle is given by the formula:
N = nC2 - n
where nC2 represents the number of ways to select 2 points from n points, and n represents the number of chords that can be formed by joining adjacent points.
In this case, we have 8 points marked on the circumference of a circle.
Number of ways to select 2 points from 8 points = 8C2 = 28
Number of chords that can be formed by joining adjacent points = 8
Therefore, the total number of chords that can be formed by joining these 8 points in pairs = 28 - 8 = 20
However, we also need to consider the chords that can be formed by joining non-adjacent points.
If we select 2 points that are not adjacent, then we can draw a diameter through those points, which will divide the circle into 2 halves.
In each half, we have 3 adjacent points and 1 non-adjacent point.
Therefore, the number of chords that can be formed by joining non-adjacent points = 2 x (3C2 - 3) = 2 x (3 - 3) = 0
Hence, the total number of chords that can be formed by joining these 8 points in pairs = 20 + 0 = 20
Therefore, the correct option is (c) 28.
To find: the number of chords obtained by joining these in pairs
Solution:
Number of chords that can be formed between n points on a circle is given by the formula:
N = nC2 - n
where nC2 represents the number of ways to select 2 points from n points, and n represents the number of chords that can be formed by joining adjacent points.
In this case, we have 8 points marked on the circumference of a circle.
Number of ways to select 2 points from 8 points = 8C2 = 28
Number of chords that can be formed by joining adjacent points = 8
Therefore, the total number of chords that can be formed by joining these 8 points in pairs = 28 - 8 = 20
However, we also need to consider the chords that can be formed by joining non-adjacent points.
If we select 2 points that are not adjacent, then we can draw a diameter through those points, which will divide the circle into 2 halves.
In each half, we have 3 adjacent points and 1 non-adjacent point.
Therefore, the number of chords that can be formed by joining non-adjacent points = 2 x (3C2 - 3) = 2 x (3 - 3) = 0
Hence, the total number of chords that can be formed by joining these 8 points in pairs = 20 + 0 = 20
Therefore, the correct option is (c) 28.
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Community Answer
8 points are marked on the circumference of a circle. The number of ch...
We are asked to find the number of chords that can be formed by joining 8 points marked on the circumference of a circle. A chord is formed by selecting two distinct points on the circle.
Step 1: Choosing 2 points from 8
To form a chord, we need to select 2 points from the 8 points marked on the circle. The number of ways to choose 2 points from 8 is given by the combination formula:
Number of chords = ι82
To form a chord, we need to select 2 points from the 8 points marked on the circle. The number of ways to choose 2 points from 8 is given by the combination formula:
Number of chords = ι82
Step 2: Apply the combination formula
The combination formula for choosing 2 points from 8 is:
ι82 = (8 × 7) / (2 × 1) = 28
The combination formula for choosing 2 points from 8 is:
ι82 = (8 × 7) / (2 × 1) = 28
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8 points are marked on the circumference of a circle. The number of chords obtained by joining these in pairs isa)25b)27c)28d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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