Prove that ,the greatest rectangle inscribed in a given circle is a square.

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

Prove that the triangle of maximum area that can be incsribed in a given circle is an equilateral triangle.

Show that of all isosceles triangles inscribed in a given circle, the equilateral triangle has the greatest area.

Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.

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

Delta ABC is an acute angle triangle inscribed in a circle in a circle .AD is a diameter of the circle . Two perpendiculars BE and CF are drawn from B and C to AC and AB respectively , which intersect each other at the point G . Prove that BDCG is a parallelogram.

Find the area of the greatest rectangle that can be inscribed in an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 .

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

Area ( in square unit) of the greatest rectangle that can be inscribed in the ellipse (x^(2))/(a^(2)) +(y^(2))/(b^(2))=1 is -

Prove that the radius of the right circular cylinder of greatest curved surface which can be inscribed in a given cone is half that of the cone.