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Geometry Level 4

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

Let ADBC,BEAC,CFABAD \perp BC, BE \perp AC, CF \perp AB and let HH be its orthocenter

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

Let r0r_0 be inradius and r1,r2,r3r_1, r_2, r_3 be the exradii of ΔABC \Delta ABC

Then find the value of

R(ABC)+R(HAB)+R(HBC)+R(HAC)+i=03ri R(ABC) + R(HAB) + R(HBC) + R(HAC) + \sum_{i=0}^3 r_i


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