If S is the circumcentre, G the centroid, O the orthocenter of  $\Delta ABC$ , then  $\overrightarrow{SA}+\overrightarrow{SB}+\overrightarrow{SC}=$ 

Let D is the midpoint of AC  $\overrightarrow{BD}=\overrightarrow{DC}\Rightarrow \overrightarrow{DB}+\overrightarrow{DC}=\overrightarrow{O}$ . We have  $2\overrightarrow{SD}=\overrightarrow{AO}$ $\overrightarrow{SA}+\overrightarrow{SB}+\overrightarrow{SC}=\overrightarrow{SA}+\left(\overrightarrow{SD}+\overrightarrow{DB}\right)+\left(\overrightarrow{SD}+\overrightarrow{DC}\right)=\overrightarrow{SA}+\overrightarrow{AO}+\overrightarrow{O}$