The lines joining the origin to the points of intersection of the line \[y=mx+c\]and the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]will be mutually perpendicular, if [Roorkee 1977]

• A. \[{{a}^{2}}({{m}^{2}}+1)={{c}^{2}}\]
• B. \[{{a}^{2}}({{m}^{2}}-1)={{c}^{2}}\]
• C. \[{{a}^{2}}({{m}^{2}}+1)={{c}^{2}}\]
• D. \[{{a}^{2}}({{m}^{2}}-1)=2{{c}^{2}}\]