The angle between the lines joining the origin to the point of intersection of  $lx+my=1$ and $x^2+y^2=a^2$ is 

• A

  $\frac{\pi }{2}$

• B

  $\frac{\pi }{4}$

• C

  ${\cos }^{-1}\left(\frac{{\displaystyle 1}}{{\displaystyle a\sqrt{l^2+m^2}}}\right)$

• D

  $2{\cos }^{-1}\left(\frac{{\displaystyle 1}}{{\displaystyle a\sqrt{l^2+m^2}}}\right)$