$\mathrm{Assertion} A:$ If $A, B, C, D$ are four points on a semi-circular arc with a centre at $O$ such that $\left|\overrightarrow{AB}\right|=\left|\overrightarrow{BC}\right|=\left|\overrightarrow{CD}\right|.$ Then, $\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}=4\overrightarrow{\mathit{A}\mathit{O}}+\overrightarrow{OB}+\overrightarrow{OC}$

$\mathrm{Reason} R:$ Polygon law of vector addition yields $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{AD}=2\overrightarrow{\mathit{A}\mathit{O}}$

In the light of the above statements, choose the most appropriate answer from the options given below.

• A

  $A$ is correct but $R$ is not correct.
• B

  $A$ is not correct but $R$ is correct.
• C

  Both $A$ and $R$ are correct and $R$ is the correct explanation of $A.$
• Correct answer
  D

  Both $A$ and $R$ are correct but $R$ is not the correct explanation of $A.$

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