Show that the straight lines `L_1=(b+c)x+a y+1=0,\ L_2=(c+a)x+b y+1=0\ n d\ L_3=(a+b)x+c y+1=0\ ` are concurrent.

Show that the straight lines L_(1)=(b+c)x+ay+1=0,L_(2)=(c+a)x+by+1=0ndL_(3)=(a+b)x+cy+1 are concurrent.

Show that the straight lines : x-y-1=0 , 4x+3y=25 and 2x-3y+1=0 are concurrent.

Consider the lines give by L_1: x+3y -5=0, L_2:3x - ky-1=0, L_3: 5x +2y -12=0

L_(1)=x+3y-5=0,L_(2)=3x-ky-1=0,L_(3)=5x+2y-12=0 are concurrent if k=

STATEMENT-1: Let DeltaABC be rigtht angle with vertices A(0,2),B(1,0)and C(0,0) if D is the point on AB such that the segment CD bisects angle C then the length of CD is (2sqrt2)/(3). STATEMENT-2: The number of points on the straight line which joins (-4,11) to (16,-1) whose co-ordinates are positve interger is 3. STATEMENT-3: If k=2 then the lines L_(1):2x+y-3=0,L_(2):5x+ky-3=0and L_(3):3x-y-2=0 are concurrent.

L_1=(a-b)x+(b-c)y+(c-a)=0L_2=(b-c)x+(c-a)y+(a-b)=0L_3=(c-a)x+(a-b)y+(b-c)=0 KAMPLE 6 Show that the following lines are concurrent L1 = (a-b) x + (b-c)y + (c-a) = 0 12 = (b-c)x + (c-a) y + (a-b) = 0 L3 = (c-a)x + (a-b) y + (b-c) = 0. ,

If the straight lines x+y-2-0,2x-y+1=0 and a x+b y-c=0 are concurrent, then the family of lines 2a x+3b y+c=0(a , b , c) are nonzero) is concurrent at (a) (2,3) (b) (1/2,1/3) (c) (-1/6,-5/9) (d) (2/3,-7/5)

If the lines x+a y+a=0,\ b x+y+b=0\ a n d\ c x+c y+1=0 are concurrent, then write the value of 2a b c-a b-b c-c adot