If the centroid of the triangle ABC is at the origin and algebraic sum of the lengths of the perpendiculars from the vertices of the triangle ABC on the variable line L is equal to 1 then sum of the squares of the reciprocals of the intercepts made by L on the coordinate axes is equal to

A(x_1, y_1), B(x_2,y_2), C(x_3,y_3) are three vertices of a triangle ABC. lx+my+n=0 is an equation of the line L. If the centroid of the triangle ABC is at the origin and algebraic sum of the lengths of the perpendicular from O the vertices of triangle ABC on the line L is equal to, then sum of the squares of reciprocals of the intercepts made by L on the coordinate axes is equal to

The algebraic sum of the perpendicular distances from the vertices of a triangle to a variable line is ‘O', then the line passes through the ------ of the triangle

If the sum of the reciprocals of the intercepts made by a line on the coordinate axes is 7 ,then the line always passes through

A variable plane moves so that the sum of the reciprocals of its intercepts on the coordinate axes is (1//2) . Then, the plane passes through the point

Let 'l' is the length of median from the vertex A to the side BC of a Delta ABC . Then

If ABC is an isosceles triangle with AB=AC .Prove that the perpendiculars from the vertices B and C to their opposite sides are equal.