Ratul's Triangle Revisited

Geometry Level 4

Suppose a triangle with side lengths \(a,b,c\) has an inradius \(r = 1\), a circumradius \(R = 3\) and a semiperimeter \(s = 7\).

Find \(a^{2} + b^{2} + c^{2}\).


Based on an imaginary question posted by Ratul Pan.
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