So Fierce

Geometry Level 4

\[ \large \sqrt{b^2-10\sqrt2 b + 51} + \sqrt{c^2-2\sqrt{14} c + 30} \leq 5 \]

Let the \(b\) and \(c\) denote the base and height of a right triangle \(ABC\), and that they satisfy the constraint above. Let the area of the triangle \(ABC\) be denoted as \(D\), find the value of \(D^2\).

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