[" 3.Fhow that the straight lines "(a-b)x+(b-c)y=c-a,(b-c)x+(c-a)y=a-b" and "],[(c-a)x+(a-b)y=b-c" are concurrent."]

Show that the straight lines (a-b)x+(b-c)y=c-a,(b-c)x+(c-a)y=a-b and (c-a)x+(a-b)y=b-c are concurrent.

Prove that the lines (b-c)x+(c-a)y+(a-b)=0, (c-a)x+(a-b)y+(b-c)=0 and (a-b)x+(b-c)y+(c-a)=0 are concurrent.

Show that the following system is inconsistent. (a-b)x+(b-c)y+(c-a)z=0 (b-c)x+(c-a)y+(a-b)z=0 (c-a)x+(a-b)y+(b-c)z=1

If ab +bc+ca=0 , show that the lines (x)/(a)+(y)/(b)=(1)/(c),(x)/(b)+(y)/(c)=(1)/(a) and (x)/(c)+(y)/(a)=(1)/(b) are concurrent.

Show that the following lines are concurrent: L_1=(a-b)x+(b-c)y+(c-a)=0 L_2=(b-c)x+(c-a)y+(a-b)=0 L_3=(c-a)x+(a-b)y+(b-c)=0

The lines a x+b y=c, b x+c y=a and c x+a y=b are concurrent, if