In a triangle $\mathrm{ABC}, a=5, b=4$ and $\tan \frac{\mathrm{C}}{2}=\sqrt{\frac{7}{9}}$, then its inradius $r=$

• Correct answer
  A

  $\frac{\sqrt{7}}{2}$
• B

  $2 \sqrt{7}$
• C

  $\frac {9}{\sqrt{7}}$
• D

  $\frac{4}{\sqrt{7}}$

Hence, the correct answer is option: 'A'.