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In an acute $\triangle ABC$, denote by $r_1,r_2,r_3$ the exradii and $k_1,k_2,k_3$ denote the respective inradii of $\triangle HBC, \triangle HCA, \triangle HAB$, then show that $r_1+r_2+r_3+k_1+k_2+k_3 = 2s$, where $s$ denotes the semi-perimeter and $H$ denotes the orthocentre of $\triangle ABC$ respectively.

I cannot show any progress here since I didn't really make any. I tried using the various common equalities like $\triangle = rs$ and stuffs relating to the exradius (using similarity/area chasing). But I didn't get anything useful.

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