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6 equally spaced girls are standing along the circumference of a circle of radius 10 m and facing the center. What is the shortest distance between any two girls facing each other?
Correct answer is '20'. Can you explain this answer?
Verified Answer
6 equally spaced girls are standing along the circumference of a circl...
Shortest distance between any 2 girls facing each other will be the diameter of the circle = 10 x 2 = 20 m
Answer: 20
Most Upvoted Answer
6 equally spaced girls are standing along the circumference of a circl...
Explanation:
To find the shortest distance between any two girls facing each other, we can draw a line connecting the center of the circle to the midpoint of the line segment joining two girls. This line will be the shortest distance between the two girls.
Step 1: Find the angle between two adjacent girls:
Since there are 6 equally spaced girls along the circumference of the circle, the angle between two adjacent girls can be calculated using the formula:
Angle between two adjacent girls = 360° / Number of girls
Angle between two adjacent girls = 360° / 6 = 60°
Step 2: Find the midpoint of the line segment:
To find the midpoint of the line segment joining two girls, we need to find the distance between two adjacent girls and divide it by 2.
Distance between two adjacent girls = Circumference of the circle / Number of girls
Circumference of the circle = 2 * π * radius
Radius = 10 m
Circumference of the circle = 2 * 3.14 * 10 = 62.8 m
Distance between two adjacent girls = 62.8 m / 6 = 10.47 m
Midpoint of the line segment = Distance between two adjacent girls / 2 = 10.47 m / 2 = 5.235 m
Step 3: Find the shortest distance:
Now, we can use the midpoint and the radius of the circle to find the shortest distance between any two girls facing each other.
Applying the Pythagorean theorem, we have:
Shortest distance = √(radius^2 + midpoint^2)
Shortest distance = √(10^2 + 5.235^2)
Shortest distance = √(100 + 27.43)
Shortest distance = √127.43
Shortest distance ≈ 11.29 m
Conclusion:
The shortest distance between any two girls facing each other is approximately 11.29 meters.
To find the shortest distance between any two girls facing each other, we can draw a line connecting the center of the circle to the midpoint of the line segment joining two girls. This line will be the shortest distance between the two girls.
Step 1: Find the angle between two adjacent girls:
Since there are 6 equally spaced girls along the circumference of the circle, the angle between two adjacent girls can be calculated using the formula:
Angle between two adjacent girls = 360° / Number of girls
Angle between two adjacent girls = 360° / 6 = 60°
Step 2: Find the midpoint of the line segment:
To find the midpoint of the line segment joining two girls, we need to find the distance between two adjacent girls and divide it by 2.
Distance between two adjacent girls = Circumference of the circle / Number of girls
Circumference of the circle = 2 * π * radius
Radius = 10 m
Circumference of the circle = 2 * 3.14 * 10 = 62.8 m
Distance between two adjacent girls = 62.8 m / 6 = 10.47 m
Midpoint of the line segment = Distance between two adjacent girls / 2 = 10.47 m / 2 = 5.235 m
Step 3: Find the shortest distance:
Now, we can use the midpoint and the radius of the circle to find the shortest distance between any two girls facing each other.
Applying the Pythagorean theorem, we have:
Shortest distance = √(radius^2 + midpoint^2)
Shortest distance = √(10^2 + 5.235^2)
Shortest distance = √(100 + 27.43)
Shortest distance = √127.43
Shortest distance ≈ 11.29 m
Conclusion:
The shortest distance between any two girls facing each other is approximately 11.29 meters.
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Community Answer
6 equally spaced girls are standing along the circumference of a circl...
If we draw a figure according to the information provided in the question then we can note that:
in the question it is good that each girl is facing the center of the circle.
radius of circle =10
diameter of circle =20
we need to find the shortest distance between any two girls face each other.
We can see from the image that oppositely standing girls will only face each other so the shortest distance between any two girls facing each other will be equal to the diameter of the circle ie 20 m
in the question it is good that each girl is facing the center of the circle.
radius of circle =10
diameter of circle =20
we need to find the shortest distance between any two girls face each other.
We can see from the image that oppositely standing girls will only face each other so the shortest distance between any two girls facing each other will be equal to the diameter of the circle ie 20 m
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