A ten – sided regular polygon is inscribed in a circle $\left|z\right|=1.A_{10},A_1,A_2,\mathrm{....},A_9$  be its vertices in anticlockwise direction with  $A_{10}=1,G_1$ is centroid of  $\Delta A_1{A}_4{A}_8,G_2$ be centroid of  $\Delta A_2{A}_6{A}_{9}and{G}_3$ be centroid of  $\Delta A_3{A}_5{A}_7$ . P is centroid of  $\Delta G_1{G}_2{G}_3$. If ‘O’ is the centre of circle