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

If a, b, c are distinct real numbers, show that the points (a, a^2), (b, b^2) and (c, c^2) are not collinear.

Show that points A (a , b + c) , B (b , c + a) , C (c , a + b) are collinear.

Show that points A (a , b + c) , B (b , c + a) , C (c , a + b) are collinear.

Show that points A (a , b + c) , B (b , c + a) , C (c , a + b) are collinear.

If a!=b!=c , prove that the points (a , a^2),(b , b^2),(c , c^2) can never be collinear.

A B C is an isosceles triangle in which A B=A C . If D\ a n d\ E are the mid-points of A B\ a n d\ A C respectively, Prove that the points B ,\ C ,\ D\ a n d\ E are concyclic.

If the points A(-1,-4),B(b , c)a n dC(5,-1) are collinear and 2b+c=4, find the values of b and c

If the position vectors of the points A,B and C be a,b and 3a-2b respectively, then prove that the points A,B and C are collinear.

If vec a ,\ vec b ,\ vec c and vec d are the position vectors of points A , B ,\ C ,\ D such that no three of them are collinear and vec a+ vec c= vec b+ vec d ,\ t h e n\ A B C D is a a. rhombus b. rectangle c. square d. parallelogram