Xét (Delta OAB) và (Delta COD) có:
(begin{array}{l}angle OBA = angle CDO = {90^o},,,,left( {gt} right)\OB = CD,,,left( {gt} right)\AB = OD,,,,left( {gt} right)\ Rightarrow Delta OAB = Delta COD,,,left( {c – g – c} right)end{array})
( Rightarrow OA = OC) (2 cạnh tương ứng)
( Rightarrow OA.OC = O{A^2} = O{B^2} + A{B^2} = {a^2} + {b^2}) (Pitago)
(begin{array}{l}cos angle AOC = cos left( {angle AOB – angle COD} right) = cos angle AOBcos angle COD + sin angle AOBsin angle COD\ = frac{{OB}}{{OA}}.frac{{OD}}{{OC}} + frac{{AB}}{{OA}}.frac{{CD}}{{OC}} = frac{{OB.OD + AB.CD}}{{OA.OC}} = frac{{ab + ab}}{{{a^2} + {b^2}}} = frac{{2ab}}{{{a^2} + {b^2}}}.end{array})
Chọn A.