A certain number of children are arranged in a circular form,if they are evenly spaced,the 7th child is directly opposite to the 8th child....

how many children are their altogether?
thanks

I think half of them must be at 0 degrees and half at 180

so how can i get the total

To solve this problem, let's break it down step by step:

1. Let's assume the total number of children is "x".
2. We know that the 7th child is directly opposite the 8th child when they are evenly spaced in a circular form.
3. When children are evenly spaced in a circular form, the distance between any two consecutive children is the same.
4. Since the 7th child is directly opposite the 8th child, their distance will be half the circumference of the circle.
5. The circumference of a circle is given by the formula C = 2πr, where "C" is the circumference and "r" is the radius.
6. Since the children are evenly spaced, the distance between any two consecutive children is equal to the radius of the circle.
7. Therefore, the distance between the 7th and 8th child is equal to half the circumference, which is πr.
8. We know that the distance between the 7th and 8th child is equal to the radius, so we can equate the two: πr = r.
9. Now we can solve for the value of "r":
πr = r
Divide both sides by "r":
π = 1
This implies that the radius "r" is zero, which means all the children are at the same position.
10. However, since we are looking for a circular arrangement with evenly spaced children, this scenario is not possible, as it would mean all the children are in the same position.
11. Therefore, there is no solution to this problem, and we cannot determine the total number of children based on the given information.

In conclusion, the question does not provide enough information to determine the total number of children.