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

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))

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

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

In a right A B C right-angled at C , if D is the mid-point of B C , prove that B C^2=4\ (A D^2-A C^2) .

In fig., if A D_|_B C , prove that A B^2+C D^2=B D^2+A C^2 .

In Figure, prove that C D+D A+A B+B C >2A C

In Figure, A C > A B\ a n d\ D is the point on A C such that A B=A Ddot Prove that B C > C D

If (a + b + c + d) (a - b - c + d) = (a + b - c - d) (a - b + c - d) , prove that: a : b = c : d .

In Figure, A D=A E\ a n d\ D\ a n d\ E are points on B C such that B D=E Cdot Prove that A B=A C

If (a)/(b) = (c)/(d) , show that : (a + b) : (c + d) = sqrt(a^(2) + b^(2)) : sqrt(c^(2) + d^(2))