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A variable line cuts n given concurrent ...

A variable line cuts n given concurrent straight lines at `A_1,A_2...A_n` such that `sum_(i=1)^n 1/(OA_i)` is a constant. Show that A,A , A such it always passes through a fixed point, O being the point of intersection of the lines

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A variable line cuts n given concurrent straight lines at A_1,A_2...A_n such that sum_(i=1)^n 1/(OA_i) is a constant. Show that it always passes through a fixed point, O being the point of intersection of the lines

A variable line cuts n given concurrent straight lines at A_1,A_2...A_n such that sum_(i=1)^n 1/(OA_i) is a constant. Show that it always passes through a fixed point, O being the point of intersection of the lines

A variable line cuts n given concurrent straight lines at A_1,A_2...A_n such that sum_(i=1)^n 1/(OA_i) is a constant. Show that it always passes through a fixed point, O being the point of intersection of the lines

If the sum of the reciprocals of the intercepts made by a variable straight line on the axes of coordinates is a constant, then prove that the line always passes through a fixed point.

Let L_1=0a n dL_2=0 be two fixed lines. A variable line is drawn through the origin to cut the two lines at R and SdotPdot is a point on the line A B such that ((m+n))/(O P)=m/(O R)+n/(O S)dot Show that the locus of P is a straight line passing through the point of intersection of the given lines R , S , R are on the same side of O)dot

Let L_1=0a n dL_2=0 be two fixed lines. A variable line is drawn through the origin to cut the two lines at R and SdotPdot is a point on the line A B such that ((m+n))/(O P)=m/(O R)+n/(O S)dot Show that the locus of P is a straight line passing through the point of intersection of the given lines R , S , R are on the same side of O)dot

Let L_1=0a n dL_2=0 be two fixed lines. A variable line is drawn through the origin to cut the two lines at R and SdotPdot is a point on the line A B such that ((m+n))/(O P)=m/(O R)+n/(O S)dot Show that the locus of P is a straight line passing through the point of intersection of the given lines R , S , R are on the same side of O)dot

Let L_1=0a n dL_2=0 be two fixed lines. A variable line is drawn through the origin to cut the two lines at R and SdotPdot is a point on the line A B such that ((m+n))/(O P)=m/(O R)+n/(O S)dot Show that the locus of P is a straight line passing through the point of intersection of the given lines R , S , R are on the same side of O)dot