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 ,D ,` respectively. Prove that `A C ,A B ,A D` 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.

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.

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.

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 AC,AB, and AD are in harmonic progression. (The three lines lie on the same side of point A.)

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

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.

A straight line through A(-15-10) meets the lines x-y-1=0,x+2y=5 and x+3y=7 respectively at A,B and C. If (12)/(AB)+(40)/(AC)=(52)/(AD) prove that the line passes through the origin.