Question

$ABCDEF$ is a regular hexagon whose centre is $O$. The $\overline{AB}+\overline{AC}+\overline{AD}+\overline{AE}+\overline{AF}$ is

• A. $2\overline{AO}$
• B. $3\overline{AO}$
• C. $5\overline{AO}$
• D. $6\overline{AO}$

Answer 1

The correct option is D $6\overline{AO}$

Since it is a regular hexagon,

$\overline{AB}=\overline{ED},\overline{AF}=\overline{CD}$

Now, $\overline{AB}+\overline{AC}+\overline{AD}+\overline{AE}+\overline{AF}=\overline{AE}+\overline{ED}+\overline{AC}+\overline{CD}+\overline{AD}=3\overline{AD}$

Now, since $O$ is the centre of the hexagon, $O$ will be the midpoint of $AD$
$\therefore 3\overline{AD}=6\overline{AO}$