Show that the area of triangle inscribed in an ellipse bears a constant ratio to the area of thetriangle formed by joining points on the auxiliary circle corresponding to the vertices of the firsttriangle.

The ratio of the area of triangle inscribed in ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 to that of triangle formed by the corresponding points on the auxiliary circle is 0.5. Then,find the eccentricity of the ellipse.(A) (1)/(2) (B) (sqrt(3))/(2) (C) (1)/(sqrt(2))(D)(1)/(sqrt(3))

prove that the area of a triangle is four times the area of the triangle formed by joining the mid-points of its sides.

The ratio of any triangle PQR inscribed in an ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and that of triangle formed by the corresponding points on the auxilliary circle is (b)/(a) .

The area of an equilateral triangle inscribed in a circle is 4sqrt(3) cm^(2) . The area of the circle is

The area of circle inscribed in an equilateral triangle of side 12 cm is

What is the area of an equilateral triangle inscribed in a circle of radius 4cm?