If 16 points are arranged in a circle, how many lines are needed to join every point at once?
To join every point at once in a circle, you need to draw lines between each pair of points. Let's calculate the number of lines needed.
For N points arranged in a circle, each point can be connected to N-1 other points. So, for 16 points, each point can be connected to 16-1 = 15 other points.
However, each line has two endpoints, so we need to divide the total number of connections by 2 to avoid counting the same line twice.
Therefore, the number of lines needed to join every point at once in a circle with 16 points is (16 * 15) / 2 = 120 / 2 = 60 lines.
To find the number of lines needed to join every point at once in a circle, we can use a simple formula.
If there are n points arranged in a circle, we can draw a line between each pair of points. However, note that any line drawn between two adjacent points will not join all the points at once since it will miss the non-adjacent points.
So, to find the number of lines needed to join every point at once, we need to draw lines between each non-adjacent pair of points. In other words, we need to connect each point to every other point that is not directly next to it.
In a circle with 16 points, each point has 15 non-adjacent points that we can connect it to. Therefore, we need to draw 15 lines from each point, resulting in a total of (16 * 15) / 2 = 120 lines.
So, the answer is 120 lines needed to join every point at once in a circle with 16 points.