Prove 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)a n d(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.

If the points (a, 0), (b,0), (0, c) , and (0, d) are concyclic (a, b, c, d > 0) , then prove that ab = cd .

If lines AB,AC,AD and AE are parallel to a line l show that points A,B,C,D and E are 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 four consecutive coefficients in any binomial expansion be a, b, c, d, then prove that (i) (a+b)/a , (b+c)/b , (c+d)/c are in H.P. (ii) (bc + ad) (b-c) = 2(ac^2 - b^2d)

If the four consecutive coefficients in any binomial expansion be a, b, c, d, then prove that (i) (a+b)/a , (b+c)/b , (c+d)/c are in H.P. (ii) (bc + ad) (b-c) = 2(ac^2 - b^2d)

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

If the segments joining the points A(a , b)a n d\ B(c , d) subtends an angle theta at the origin, prove that : cos theta=(a c+b d)/sqrt((a^2+b^2)(c^2+d^2))