Let  $1,{\alpha }_1,{\alpha }_2,{\alpha }_3,{\alpha }_4$  be the 5th roots of unity. If  $A_1,A_2,A_3,A_4,A_5$   are vertices of a polygon formed by  $1,{\alpha }_1,{\alpha }_2,{\alpha }_3,{\alpha }_4$ on complex plane then which of following statement(s) is/are correct :

Product  $\left(A_1{A}_2\right)\left(A_1{A}_3\right)\left(A_1{A}_4\right)\left(A_1{A}_5\right)\left(A_2{A}_3\right)\left(A_2{A}_4\right)\left(A_2{A}_5\right)\left(A_3{A}_4\right)\left(A_4{A}_5\right)$   is equal to  ${\left(\sqrt{5}\right)}^5$   where  $A_i{A}_j$   is length of line segment joining $A_i$ and  $A_j$

${\left(A_1{A}_2\right)}^2+{\left(A_1{A}_3\right)}^2+{\left(A_1{A}_4\right)}^2+{\left(A_1{A}_5\right)}^2=10$

Area of the circle inscribed in the polygon is  $\frac{\pi }{2}(1+\cos \frac{2\pi }{5})$

$(1+{\alpha }_1)(1+{\alpha }_2)(1+{\alpha }_3)(1+{\alpha }_4)=0$