Show that if any line through the variable point `A(k+1,2k)` meets the lines `7x+y-16=0,5x-y-8=0,x-5y+8=0` at `B ,C ,D ,` respectively, the `A C ,A B ,a n dA D` are in harmonic progression. (The three lines lie on the same side of point `Adot)dot`

A Line through the variable point A(1+k,2k) meets the lines 7x+y-16=0, 5x-y-8=0 and x-5y+8=0 at B,C,D respectively. Prove that AC,AB and AD are in HP.

A line through the variable point A(k+1,2k) meets the lines 7x+y-16=0,quad 5x-y-8=0,x-5y+8=0 at B,C,D, respectively.Prove that AC,AB,AD are in HP.

Which of the following is / are CORRECT (A) If the points A (x,y+z) , B (y,z+x) and C (z,x+y) are such that AB=BC , then x, y, z are in A.P. (B) If a line through the variable point A (k+1, 2k) meets the lines , 7x+y-16=0 , 5x-y-8=0 , x-5y+8=0 at B , C and D Respectively, then AC , AB and AD are in H.P.

A straight line through origin O meets the lines 3y=10-4x and 8x+6y+5=0 at point A and B respectively. Then , O divides the degment AB in the ratio.

Find the equation of the line passing through the point P(1,2) cutting the lines x+y-5=0 and 2x-y=7 at A and B respectively such that the H.M. of PA and PB is 10.(A,B lie on the same side of P)

The orthocentre of the triangle formed by the lines x-7y+6=0,2x-5y-6=0 and 7x+y-8=0 is

The line 2x+3y=6, 2x+3y-8 cut the X-axis at A,B respectively. A line L=0 drawn through the point (2,2) meets the X-axis at C in such a way that abscissa of A,B,C are in arithmetic Progression. then the equation of the line L is