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Geometry Level 4

Consider \( \Delta ABC \) such that \(AB = 13, BC = 14, AC = 15 \)

Let \(AD \perp BC, BE \perp AC, CF \perp AB \) and let \(H\) be its orthocenter

Let \(R(ABC)\) denote circumradius of \( \Delta ABC \)

Let \(r_0 \) be inradius and \(r_1, r_2, r_3 \) be the exradii of \( \Delta ABC \)

Then find the value of

\[ R(ABC) + R(HAB) + R(HBC) + R(HAC) + \sum_{i=0}^3 r_i \]

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