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

• May 15th 2012, 09:00 AM
dgu
Is 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, 09:45 AM
emakarov
Re: 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, 11:11 AM
Wilmer
Re: 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?