SEAMO 2027 - Paper D - SET 02 - Self-study Question 12

Question 12

An equilateral triangle $ABC$ has area $\sqrt3$ and side length 2. The point $P$ is anywhere in its interior. What is the sum of the distances from $P$ to $AB$, $AC$ and $BC$?

$1$
$\sqrt3$
$\frac12$
$\frac{\sqrt3}{2}$
$\frac{\sqrt3}{3}$