A variable line is drawn through \( O \), to cut two fixed straight lines \( L_{1} \) and \( L_{... VIDEO
A variable line is drawn through \( O \), to cut two fixed straight lines \( L_{1} \) and \( L_{2} \) in \( A_{1} \) and \( A_{2} \), respectively.
A point \( A \) is taken on the variable line such that \( \frac{m+n}{O A}=\frac{m}{O A_{1}}+\frac{n}{O A_{2}} \).
Show that the locus of \( A \) is a straight line passing through the point of intersection of \( L_{1} \) and \( L_{2} \) where \( O \) is being the origin.
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\begin{array}{l}
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