Is it possible to find out the length of X in this diagram?

Attachment 23873

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- May 15th 2012, 08:00 AMdguIs it possible to find out the length of X in this diagram?
Is it possible to find out the length of X in this diagram?

Attachment 23873

Thanks! - May 15th 2012, 08:45 AMemakarovRe: Is it possible to find out the length of X in this diagram?
I assume these are squares inscribed in circles. Let the circle radius be r. From trigonometry or Pythagorean theorem it follows that half of the square side is r * sqrt(2) / 2, so x = r(1 - sqrt(2) / 2). We also have 4r - 2x = 100, from where r and then x can be found.

- May 15th 2012, 10:11 AMWilmerRe: Is it possible to find out the length of X in this diagram?
...or, the given 100 being h, general case:

x = h(1 - f) / 2 where f = 2SQRT(2) / [2 + SQRT(2)]

As Mr Makarov says, squares inside the circles are assumed.

r = radius, k = squares side length.

You have:

h = 2k + 2x : x = (h - 2k) / 2

and:

r - x = k/2 : x = (2r - k) / 2

So h - 2k = 2r - k

And since r = k / SQRT(2), you can easily get x in terms of h.

Good nuff?