# Show that the sum of inradii and exradii of $\Delta HX_iX_j$ where $X_k \in \{A,B,C\}$ of $\Delta ABC$ and its orthocentre $H$.

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.