Rectangles are inscribed inside a semi-circle of radius `rdot` Find the rectangle with maximum area.

The area of the triangle inscribed in a circle of radius 4 and the ratio of its angles in the ratio 5:4:3 is

Regular pentagons are inscribed in two circles of radius 5 and 2 units respectively. The ratio of their areas is

A rectangle of area y cm^2 is inscribed in a circle of radius 25 cm. If the length of a side of the rectangle be x cm, find y in terms of x.

Prove that an angle inscribed in a semi-circle is a right angle using vector method.

Show that of all the rectangles inscribed in a given fixed circle, the square has the maximum area.

The length of the rectangle of maximum area that can be inscribed in a semicircle of radius 1 unit, so that two vertices lie on the diameter, is-

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

ABC is an isosceles triangle inscribed in a circle of radius rdot If A B=A C and h is the altitude from A to B C , then triangle A B C has perimeter P=2(sqrt(2h r-h^2)+sqrt(2h r)) and area A= ____________ and = __________ and also ("lim")_(h vec 0) A/(P^3)=______

By vector method show that , an angle inscribed in a semi - circle is a right angle ,