# Thread: where to draw a line

1. ## where to draw a line

Draw a line across the figure so that the total area of the circles is divided exactly in half.

thanks guys

2. ## Re: where to draw a line

Clearly, each region is going to have an area of 2 1/2 circles. You could simply draw a vertical line through the middle two circles such that the area is bisected...then you could compute the perpendicular distance between the line and the centers of the middle two circles.

3. ## Re: where to draw a line

This will do it:

4. ## Re: where to draw a line

^Or that. Nice.

5. ## Re: where to draw a line

For unit circles richards vertical moved 0.4 units to the left bisects the circle area of the five circles. Result calculated using segment area tabulated values based on 1 semi circle where the desired area is pi/4

6. ## Re: where to draw a line

Originally Posted by bjhopper
For unit circles richards vertical moved 0.4 units to the left bisects the circle area of the five circles. Result calculated using segment area tabulated values based on 1 semi circle where the desired area is pi/4
This is not accurate. At an offset of 0.4 the approximate area of the segment is pi x 0.252316. It's certainly possible to calculate the correct position of the vertical line to greater accuracy, but you'd be hard pressed to actually draw the correct position of the vertical line to exactly cut the area in half.

7. ## Re: where to draw a line

Would you believe an offset of 0.404 ?