The largest area of the trapezium inscribed in a semi-circle or radius `R ,` if the lower base is on the diameter, is (a) `(3sqrt(3))/4R^2` (b) `(sqrt(3))/2R^2` `(3sqrt(3))/8R^2` (d) `R^2`

A rectangle is inscribed in an equilateral triangle of side length 2a units. The maximum area of this rectangle can be (a) sqrt(3)a^2 (b) (sqrt(3)a^2)/4 a^2 (d) (sqrt(3)a^2)/2

The eccentricity of ellipse, if the distance between the foci and L.R is same a. (sqrt(3))/2 b. 2/(sqrt(3)) c. 1/(sqrt(2)) d. (sqrt(5)-1)/2

Three equal circles each of radius r touch one another. The radius of the circle touching all the three given circles internally is (2+sqrt(3))r (b) ((2+sqrt(3)))/(sqrt(3))r ((2-sqrt(3)))/(sqrt(3))r (d) (2-sqrt(3))r

In Fig. 15.111, if A B C is an equilateral triangle, then shaded area is equal to (FIGURE) (a) (pi/3-(sqrt(3))/4)r^2 (b) (pi/3-(sqrt(3))/2)r^2 (c) (pi/3+(sqrt(3))/4)r^2 (d) (pi/3+sqrt(3))r^2

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 6sqrt(3)r

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)

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) .

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) .

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) .

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 6sqrt3r .