Let ABC be an arbitrary triangle.

Let A_B and A_C be the orthogonal projections of A onto the internal bisectors of angles B and C respectively.

Let B_C and B_A be the orthogonal projections of B onto the internal bisectors of angles C and A respectively.

Let C_A and C_B be the orthogonal projections of C onto the internal bisectors of angles A and B respectively.

Prove that |A_BA_C| + |B_CB_A| + |C_AC_B| = s,

where s is the semiperimeter of triangle ABC.