Prove that the straight lines `ax+(b+c)y+d=0,bx+(c+a)y+d=0andxc+(a+b)y+d=0` are concurrent.

If a,b,c are in A.P.prove that the straight lines ax+2y+1=0,bx+3y+1=0 and cx+4y+1=0 are concurrent.

Prove that the straight lines ax+by+c=0,bx+cy+a=0and cx+ay+b=0 are concurrent if a+b+c=0.When a!=b!=c .

If a ,\ b ,\ c are in A.P. prove that the straight lines a x+2y+1=0,\ b x+3y+1=0\ a n d\ c x+4y+1=0 are concurrent.

If the straight lines ax + by + c= 0 , bx +cy + a = 0 and cx +ay + b =0 are concurrent , then prove that a^(3)+b^(3)+c^(3)=3abc .

If the three straight lines ax + 2y + 1 = 0, 3y + bx + 1 = 0 and cx+ 4y + 1=0 are concurrent, then show that- a. b, c are in AP.

If ab+bc+ca=0 then prove that the straight lines x/a+y/b=1/c,x/b+y/c=1/aand x/c+y/a=1/b are concurrent.

The three lines a x+b y+c=0, b x+c y+a=0 and c x+a y+b=0 are concurrent only when

If the straight lines ax+by+c=0, bx+cy+a=0 and cx+ay+b=0 are concurrent, then prove that a^(3)+b^(3)+c^(3)=3abc