At the endpoint and midpoint of a circular are AB, tangent lines are drawn, and the points, A and B are jointed with a chord. Prove that the ratio of the areas of the triangles thus formed tends to 4 as the arc AB decreases infinitely.

From the point (-1, 2), tangent lines are drawn to the parabola y^2= 4x . Find the equation of the chord of contact. Also find the area of the triangle formed by the chord of contact and the tangents.

. Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is

In a triangle ABC, a line is drawn from C which bisects AB at point D. Find the ratio of area of the triangles DBC and ABC.

In Delta ABC, D and E are the midpoint of AB and AC respectively. Find the ratio of the areas of Delta ADE and Delta ABC .

In the picture below, the top vertex of a triangle is joined to the midpoint of the bottom side of the triangle and then the midpoint of this line is joined to the other two vertices. Prove that the areas of all four triangles obtained thus are equal to a fourth of the area of the whole triangle.