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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.