The point `A_(1),A_(2)…… A_(10)` are equally distributed on a circle of radius R (taken in order). Prove that ` A_(1)A_(4) -A_(1)A_(2) =R`

Let A_(1)A_(2)A_(3)………………. A_(14) be a regular polygon with 14 sides inscribed in a circle of radius 7 cm. Then the value of (A_(1)A_(3))^(2) +(A_(1)A_(7))^(2) + (A_(3)A_(7))^(2) (in square cm) is……………..

Let A_(1),A_(2),A_(3),.........,A_(14) be a regular polygon with 14 sides inscribed in a circle of radius R. If (A_(1)A_(3))^(2)+(A_(1)A_(7))^(2)+(A_(3)A_(7))^(2)=KR^(2) , then K is equal to :

A_(0),A_(1),A_(2),A_(3),A_(4),A_(5) be a regular hexagon inscribed in a circle of unit radius,then the product of (A_(0)A_(1)*A_(0)A_(2)*A_(0)A_(4) is equal to

let A_(1),A_(2),A_(3),...A_(n) are the vertices of a regular n sided polygon inscribed in a circle of radius R.If (A_(1)A_(2))^(2)+(A_(1)A_(3))^(2)+...(A_(1)A_(n))^(2)=14R^(2) then find the number of sides in the polygon.

Let A_(0)A_(1)A_(2)A_(3)A_(4)A_(5) be a regular hexagon inscribed in a circle of unit radius.Then the product of the lengths the line segments A_(0)A_(1),A_(0)A_(2) and A_(0)A_(4) is

If A,A_(1),A_(2) and A_(3) are the areas of the inscribed and escribed circles of a triangle, prove that (1)/(sqrt(A))=(1)/(sqrt(A_(1)))+(1)/(sqrt(A_(2)))+(1)/(sqrt(A_(3)))

n equidistant points A_(1), A_(2), A_(3) ………A_(n) are taken on base BC of DeltaABC is A_(1)B=A_(1)A_(2)=A_(n)C and area of DeltaA""A_(4)A_(5) is k cm^(2) , then what is the area of DeltaABC .

Five boys A_(1),A_(2),A_(3),A_(4),A_(5) , are sitting on the ladder in this way -A_(5) is above A_(1),A_(3) under A_(2),A_(2) , under A_(1) and A_(4) above A_(3) . Who sits at the bottom?