How do I prove $IH^2 = 2r^2 - 2Rr_p$ , where $I$ is the incentre of a triangle, $H$ is the orthocentre, $r$ is the inradius, $R$ is the circumradius and $r_p$ is the inradius of the orthic triangle of triangle $ABC$?
I think using coordinates. Idk if complex numbers make it easy (because I'm unknown). Synthetic clearly seems to last ...