## Cyclic Lattice Points

For any positive integer \(N \geq 2\), let \(D(N)\) denote the diameter of the smallest circle which passes through exactly \(N\) different lattice points. For example:

- \(D(2) = 1.0\)
- \(D(3) = \frac{5}{3}\sqrt{2} = 2.3570226039551585\ldots\)
- \(D(4) = \sqrt{2} = 1.4142135623730951\ldots\)

Part A | What are the first \(6\) digits of \(D(8)\) after the decimal point? | |
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Part B | What are the first \(6\) digits of \(D(5)\) after the decimal point? |