Need help with a geometry/maths problem

A square of whose sides are 1, has 3 circles of equal size inscribed in it, with no overlap. What is the diameter or radius of these circles?

picture of problem, look at the one with 3 circles. http://mathworld.wolfram.com/images/eps-…

First, draw a line from the lower left corner of the square to the top right corner of the square. The cluster of circles are symmetric about this line.

Now, since the circles are of equal size, a triangle formed by drawing a line from the center of each circle to the centers of the other triangles is a 60 degree equilateral triangle with three sides of length 2*radius. This triangle is also symmetric about the square's diagonal.

Let's focus on the triangle edge that connects the two lower circles. The "slope" of this line can be calculated knowing that the square diagonal bisects the left-most 60 degree corner of the triangle. The angle of the diagonal is 45 degrees, the angle of the triangle's bottom edge is 30 degrees (half of 60) with respect to the diagonal, so it forms a slope 15 degrees with respect to the bottom of the square.

Now draw two lines: one perfectly horizontal from the center of the lower left circle to the left edge of the square, and one perfectly horizontal from the center of the right circle to the right edge of the square. These lines show a "path" of radial distances across the square.

Finally, use trigonometry to find the distance of this path, knowing that the length of a side of the square is 1:

1 = r [first perfectly horizontal line] + cos15*(2r) [the horizontal component of the bottom edge of the triangle] + r [second perfectly horizontal line]

Simplified: 1 = 2r + 2r*cos15
1 = 2r*(1+cos15)
1 / (2(1+cos15)) = r
0.254 = r

So the radius of each circle is 0.254.

you can take 0.3333 radius