# 400 followers problem!

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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