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A(x(1),y(1)),B(x(2),y(2)),C(x(3),y(3)) a...

`A(x_(1),y_(1)),B(x_(2),y_(2)),C(x_(3),y_(3))` are the vertices of a triangle ABC and `ax+by+c=0` is the equation of the line L, then answer the following questions.
If the centroid of the triangle ABC is at the origin and algebraic sum of the length of the perpendicular from the vertices of the triangle on the line L is equal to 1, then prove that sum of the squares of the reciprocal of intercepts made by L on the co-ordinate axes is `9`.

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The correct Answer is:
9
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