$|\overrightarrow{A B}|=|\overrightarrow{B C}|=|\overrightarrow{C D}|$

Here, $O$ is the centre of semi- circle

$\therefore|\overrightarrow{O A}|=|\overrightarrow{O B}|=|\overrightarrow{O C}|=|\overrightarrow{O D}|$

Using vector law of addition, we can write,

$\overrightarrow{ AB }=\overrightarrow{ AO }+\overrightarrow{ OB }$

$\overrightarrow{ AC }=\overrightarrow{ AO }+\overrightarrow{ OC }$

$\overrightarrow{ AD }=\overrightarrow{ AO }+\overrightarrow{ OD }=2 \overrightarrow{ AO }$

After adding all, we get,

$\overrightarrow{A B}+\overrightarrow{A C}+\overrightarrow{A D}=4 \overrightarrow{A O}+\overrightarrow{O B}+\overrightarrow{O C}$

Reason $R$ is the direct result of Polygon law of vector addition

Therefore, Polygon law is applicable in both but the equation given in the reason is not useful in explaining the assertion.