The equation of the circle which touches the circle $\mathrm{S} \equiv x^2+y^2-10 x-4 y+19=0$ at the point $(2,3)$ internally and having radius equal to half of the radius of the circle $\mathrm{S}=0$ is

• A

  $x^2+y^2+7 x+5 y+64=0$
• Correct answer
  B

  $x^2+y^2-7 x-5 y+16=0$
• C

  $x^2+y^2-14 x-10 y+16=0$
• D

  $x^2+y^2-5 x-7 y+16=0$

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