`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

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 the vertices of a triangle ABC. lx+my+n=0 is an equation of the line L. Answer the following questions based on above passage : If the centroid of the triangle ABC is at the origin and algebraic sum of the length of the perpendiculars from the vertices of the triangle ABC on the line L is equal to 1 then sum of the squares of the intercepts made by L on the coordinate axes is equal to

If A(x_1,y_1),B(x_2,y_2),C(x_3,y_3) are the vertices of the triangle then find area of triangle

If A(x_1,y_1),B(x_2,y_2) and C(x_3,y_3) are the vertices of triangleABC ,find the coordinates of the centroid of the triangle.

The points A (x_(1),y_(1)), B (x_(2),y_(2)) and C (x_(3),y_(3)) are the vertices of Delta ABC . What are coordinate of the centroid of the triangle ABC ?

If A(1,a),B(a,a^(2)) and C(a^(2),a^(2)) are the vertices of a triangle which are equidistant from the origin,then the centroid of the triangle ABC is at the point

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 P divides BC in the ratio 2:1 and Q divides CA in the ratio 1:3 then R divides AB in the ratio (P,Q,R are the points as in problem 1)