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First divide the regular octagon into  8 isoceles triangles
  thus angle of 1 triangle at the center of the circle  =
      360/8  = 45°       
      then draw a perpendicular line from the apex of a triangle
      to the mid-point of one side of the octagon which will divide
       the triangle into 2 right triangles, each having angle 45/2 =22.5° since it's an inscribed octagon the hypothenuse of the rtΔ is the radius of the circle

         ∴  sin  22.5° =   x/10
              x =  10*sin 22.5   = 10*  0.3826
                                          =  3.826
                Thus the length of one side of the octagon = 2* 3.826
                                                                                     ≈  7.652 cm
                 you will understand me better if you can draw the circle
                 and octagon
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