[tex]\it \overline{AM} +\overline{BN}+\overline{CP}=\dfrac{\overline{AB}+\overline{AC}}{2}+\dfrac{\overline{BA}+\overline{BC}}{2}+\dfrac{\overline{CA}+\overline{CB}}{2}=\\ \\ \\ =\dfrac{\overline{AB}+\overline{BA}+\overline{AC}+\overline{CA}+\overline{BC}+\overline{CB}}{2}=\dfrac{\overline0+\overline0+ \overline0}{2}= \overline0[/tex]
