`A_(1), A_(2), A_(3),...,A_(n)` is a regular polygon of n side circumscribed about a circle of centre O and radius 'a'. P is any point distanct 'c' from O. Show that the sum of the squares of the perpendiculars from P on the sides of the polygon is n `(a^(2)+ (c^(2))/(2)).`

If A_(1), A_(2),..,A_(n) are any n events, then

Given that the area of a polygon of n sides circumscribed about a circle is to the area of the circumscribed polygon of 2n sides as 3:2 find n.

Find the radius of the circumscribing circle of a regular polygon of n sides each of length is a.

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 R is the radius of circumscribing circle of a regular polygon of n-sides,then R =

Prove that the area of a regular polygon hawing 2n sides, inscribed in a circle, is the geometric mean of the areas of the inscribed and circumscribed polygons of n sides.

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

A polygon of n sides, inscribed in a circle, is such that its sides subtend angle 2 alpha, 4 alpha,…,2n alpha at the centre of the circles. Prove that its area A_(1), is to the area A_(2) of the regular polygon of n iseds inscribed in the same circle, as sin n alpha : n sin alpha.

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 which area of A_(n) is less than 1.

If I_n is the area of n sided regular polygon inscribed in a circle of unit radius and O_n be the area of the polygon circumscribing the given circle, prove that I_n=(O_n)/2(1+(sqrt(1-((2I_n)/n)^2))