A circle is inscribed in an n-sided regular polygon `A_1, A_2, …. A_n` having each side a unit for any arbitrary point P on the circle, pove that `sum_(i=1)^(n)(PA_i)^2=n(a^2)/(4)(1+cos^2((pi)/(n)))/(sin^2((pi)/(n)))`

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))

I_(n) is the area of n sided refular polygon inscribed in a circle 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)))

If r is the radius of inscribed circle of a regular polygon of n-sides ,then r is equal to

The area of the circle and the area of a regular polygon of n sides and the perimeter of polygon equal to that of the circle are in the ratio of tan(pi/n):pi/n (b) cos(pi/n):pi/n sinpi/n :pi/n (d) cot(pi/n):pi/n

Let A_n be the area that is outside a n-sided regular polygon and inside its circumscribeing circle. Also B_n is the area inside the polygon and outside the circle inscribed in the polygon. Let R be the radius of the circle circumscribing n-sided polygon. On the basis of above information, answer the equation If n=6\ then A_n is equal to R^2((pi-sqrt(3))/2) (b) R^2((2pi-6sqrt(3))/2) R^2(pi-sqrt(3)) (d) R^2((2pi-3sqrt(3))/2)

The difference between an exterior angle of (n-1) sided regular polygon and an exterior angle of (n+2) sided regular polygon is 6^(@) . Find the value of n

A_(1),A_(2), …. A_(n) are the vertices of a regular plane polygon with n sides and O ars its centre. Show that sum_(i=1)^(n-1) (vec(OA_(i))xxvec(OA)_(i+1))=(n-1) (vec(OA)_1 xx vec(OA)_(2))

A_1,A_2,..., A_n are the vertices of a regular plane polygon with n sides and O as its centre. Show that sum_(i=1)^n vec (OA)_i xx vec(OA)_(i+1)=(1-n)(vec (OA)_2 xx vec(OA)_1)

The area of a regular polygon of n sides is (where r is inradius, R is circumradius, and a is side of the triangle (a) (n R^2)/2sin((2pi)/n) (b) n r^2tan(pi/n) (c) (n a^2)/4cotpi/n (d) n R^2tan(pi/n)

The area of a regular polygon of n sides is (where r is inradius, R is circumradius, and a is side of the triangle) (n R^2)/2sin((2pi)/n) (b) n r^2tan(pi/n) (n a^2)/4cotpi/n (d) n R^2tan(pi/n)