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Geometry Problem. Post your solution in the comment box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the diagram below to enlarge it.
By construction, y = OO1 = 1-OB = 1-√2/2. x is to OB-y as y is to √2/2, hence x=3-2√2
Let R is the radius of circles O1 and O2Along diagonal AC we have AC= 2.R+2.R.sqrt(2)= sqrt(2)So R= 1/(2.(1+sqrt2))Along Diagonal BD we have BD= 2.R+2.x+ 2.x.sqrt(2)= sqrt(2)Replace value of R in above we get x= 3-2.sqrt(2)