# where to draw a line

• Aug 6th 2012, 07:31 AM
rcs
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
• Aug 6th 2012, 08:45 AM
richard1234
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.
• Aug 6th 2012, 08:55 AM
ebaines
Re: where to draw a line
This will do it: :)
• Aug 6th 2012, 09:05 AM
richard1234
Re: where to draw a line
^Or that. Nice.
• Aug 7th 2012, 02:55 PM
bjhopper
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
• Aug 8th 2012, 05:00 AM
ebaines
Re: where to draw a line
Quote:

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.
• Aug 8th 2012, 05:39 AM
bjhopper
Re: where to draw a line
Would you believe an offset of 0.404 ?