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.

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 A(-5,-4) meets the lines x+3y+2=0,2x+y+4=0a n dx-y-5=0 at the points B , Ca n dD respectively, if ((15)/(A B))^2+((10)/(A C))^2=(6/(A D))^2 find the equation of the line.

A line through A(-5,-4) meets the lines x+3y+2=0,2x+y+4=0a n dx-y-5=0 at the points B , Ca n dD rspectively, if ((15)/(A B))^2+((10)/(A C))^2=(6/(A D))^2 find the equation of the line.

A line through A(-5,-4) meets the lines x+3y+2=0,2x+y+4=0a n dx-y-5=0 at the points B , Ca n dD rspectively, if ((15)/(A B))^2+((10)/(A C))^2=(6/(A D))^2 find the equation of the line.

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 Segment 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.

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

A circle having centre at C is made to pass through the point P(1,2), touching the straight lines 7x-y=5 and x+y+13=0 at A and B respectively. Then

Prove that the three lines 2x-y-5=0, 3x-y-6=0 and 4x-y-7=0 meet in a point.