If `A_(1),A_(2),A_(3)` denote respectively the areas of an inscribed polygon of 2n sides , inscribed polygon of n sides and circumscribed poylgon of n sides ,then `A_(1),A_(2),A_(3)` are in

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_(1),A_(2),A_(3)...,A_(n) are the vertices of a polygon ofnsides.If the number of pentagons that can beconstructed by joining these vertices such that none of the side of the polygon is also the side ofthe pentagon is 36, then the value of 'n' is :

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……………..

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)))

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 :

Let A_(1), A_(2), A_(3),….., A_(n) be squares such that for each n ge 1 the length of a side of A _(n) equals the length of a diagonal of A _(n+1). If the side of A_(1) be 20 units then the smallest value of 'n' for wheich area of A_(n) is less than 1.

A regular pentagons is inscribed in a circle. If A_(1) and A_(2) represents the area of circle and that of regular pentagon respectively, then A_(1) : A_(2) is