KöMaL 2010 A497

There is given an acute triangle ABC in the plane. Denote by $A_1$, $B_1$ and $C_1$ the perpendicular feet of an arbitrary interior point $P$ of the triangle on the sides $BC$, $CA$and $AB$, respectively. Let the inradii of the triangles PAC $_1$, $PC_1 B$, PBA $_1$, $PA_1 C$, PCB $_1$ and $PB_1 A$ be $\varrho_1$,$\varrho_2$,...,$\varrho_6$, respectively. Determine the locus of those points $P$ for which $\varrho_1$+$\varrho_3$+$\varrho_5$=$\varrho_2$+$\varrho_4$+$\varrho_6$.