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The triangle APB is an equilateral triangle.  Because  APB is 60 deg.  ABP and PAB are 60 deg each, because  AP = BP and  hence ABP and PAB are both equal.

Now AOP is a right angle triangle.  AO = b / root(2)
     OP = h                AP = b, and  is the hypotenuse
   b² = h² + b²/2    =>     2 h² = b²

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