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

_{B}A

_{C}| + |B

_{C}B

_{A}| + |C

_{A}C

_{B}| = s,

where s is the semiperimeter of triangle ABC.