InterviewSolution
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InterviewSolution
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The algebraic sum of the perpendicular distances from `A(x_1, y_1)`, `B(x_2, y_2)` and `C(x_3, y_3)` to a variable line is zero. Then the line passes through (A) the orthocentre of `triangleABC` (B) centroid of `triangleABC` (C) incentre of `triangleABC` (D) circumcentre of `triangleABC`A. the orthocentre of `Delta ABC`B. the centroid of `Delta ABC `C. the circumcentre of `DeltaABC`D. none of these |
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Answer» Correct Answer - B Let `Px + Qy = 1` be a variable line, where P,Q are variable. By hypothesis , we have . `(Px_(1)+Qy_(1)-1)/(sqrt(p^(2) +Q^(2)) +(p^(2)+Q^(2)))+(Px_(3)+Qy_(3)-1)/(sqrt(P^(2)+Q^(2)))=0` `rArr P(x_(1) + x_(2) + x_(3)) +Q(y_(1) + y_(2)+y_(3)) = 3` `rArr p((x_(1)+x_(2)+x_(3))/(3))+Q((y_(1)+y_(2)+y_(3))/(3))=1` `rArr ((x_(1) + x_(2)+x_(3))/(3),(y_(1)+y_(2)+y_(3))/(3))` lies on `Px + Qy=1` Hence, the variable line passig thorought the the centriod of the triangle ABC. |
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