Prove that the points (a, b), (c, d) and (a-c, b-d) are collinear, if ad = bc.

Show that the points (a, b), (c, d) and (a - c, b - d) are collinear if ad = bc.

Prove that the points (a,b+c),(b,c+a) and (c,a+b) are collinear.

Prove that the points (a+b+c),(b,c+a) and (c,a+b) are collinear.

Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.

Prove that the points (a ,b+c),(b ,c+a)a n d(c ,a+b) are collinear.

Prove that the points (a ,b+c),(b ,c+a)a n d(c ,a+b) are collinear.

Prove that the points (a,bc-a^(2)),(b,ca-b^(2)),(c,ab-c^(2)) are collinear.

In the given figure,AE =DE and BC|AD . Prove that the points A,B,C and D are concyclic.Also,prove that the diagonals of the quadrilateral ABCD are equal.