Algebra and Geometry Don't Fit Well!

Geometry Level 5

2x3=y2=2z23\large \dfrac {2x}{\sqrt 3} = y \sqrt 2 = \dfrac {2z}{\sqrt {2-\sqrt 3}}

Consider a triangle with side lengths xx, yy and zz satisfying the equation above. If the longest side has length 303, then the circumradius of this triangle can be expressed as aba \sqrt b, where aa and bb are positive integers with bb square-free. Find a+ba+b.

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