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9th Class Mathematics Geometry Question Bank Geometry

  • question_answer
    ABC is a triangle. A line PQ intersects the sides AB and AC in points P and Q such that \[\frac{AP}{PB}=\frac{AQ}{QC}=\frac{m}{n}.\,\,\,m,\,\,n\] being positive integers. The line PQ will pass through the centre of gravity of the triangle if the value of m, n respectively is

    A)   2, 3                     

    B)  1 , 2                  

    C)  1 , 3                

    D)  2, 1                 

    Correct Answer: D

    Solution :

     Let G be the centre of gravity of \[\Delta \,ABC\] From similar \[\Delta \,s\] APG and ABR,                                 \[\frac{AP}{AB}=\frac{AG}{AR}\]                 or            \[\frac{AP}{AB-AP}=\frac{AG}{AR-AG}\]                 or            \[\frac{AP}{PB}=\frac{AG}{GR}\]                 \[\therefore \]  \[\frac{m}{n}=\frac{2}{1}\] Hence    \[m=2\] and          \[n=1\]


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