If ` a : b = c : d `, then prove that `(a +b)/(a - b) = sqrt(ac + ad + bc + bd)/sqrt(ac - ad - bc + bd)`.

If (ad-bc)/(a-b-c+d) = (ac-bd)/(a-b+c-d) then show that each ratio = (a+b+c+d)/4

If in the cyclic quadrilateral AB||CD , then prove that AD =BC and AC=BD.

IF ad ne bc then the roots of (a^2 +b^2)x^2+2x(ac+bd) +(c^2 +d^2)=0 are

If (ad -bd)/(a-b-c+d) =(ac-bd)/(a-b-d+c) , then show that each ratio is equal to (a+b+c+d)/4 .

If Rs.x are divided between A and B in the ratio (a)/(b);(c)/(d) then A gets rupees (adx)/(ab+cd)b(adx)/(ad+bc) c.(abx)/(ad+bc)d.(abx)/(ac+bd)

In Delta ABC , BD : CD = 3 : 1 and AD _|_ BC . Prove that 2(AB^(2) - AC^(2)) = BC^(2) .

If a and b are positive natural numbers (sqrt(a)+sqrt(b))(sqrt(c)+sqrt(d))=sqrt(ac)+sqrt(ad)+sqrt(bc)+sqrt(bd)