" 16.Prove that "{{a},{a,b}}={{c},{c,d}}" iff "a=c" and "b=d

Prove that [a xx b,a xx c,d]=(a*d)[a,b,c]

If a,b,c and d are in H.P.,then prove that (b+c+d)/a,(c+d+a)/b,(d+a+b)/c and (a+b+c)/d, are in A.P.

If a,b,c,d are in G.P., then prove that: (b-c)^2 + (c-a)^2+(d-b)^2=(a-d)^2

If a, b, c and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .

If a, b, c and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .

If a, b, c and d are four coplanr points, then prove that [a b c]=[b c d]+[a b d]+[c a d] .

Is R an equivalence relation in the set NxxN which is defined as (i) (a,b)R(c,d) iff a+d=b+c (ii) (a,b)R(c,d) iff ad=bc for all (a,b),(c,d) in NxxN ?

If a, c, b are in A.P. and b, c, d are in G.P. prove that, b, (b-c), (d-a) are in G.P.

In Figure, A D=B C\ a n d\ B D=C A . Prove that ∠A D B= ∠B C A a n d ∠D A B=∠ C B A .

In A B C , ray A D bisects /_A and intersects B C in D . If B C=a , A C=b and A B=c , prove that B D=(a c)/(b+c) (ii) D C = (a b)/(b+c)