MathNet 2021 — Part 07 Question 14

Question 14

Let $ABC$ be an equilateral triangle with side length one, and let $P$ lie on the opposite side of line $AB$ from $C$, with $\angle APB=60^\circ$. Suppose that the bisector of $\angle APB$ meets segments $AB$ and $AC$ at $X$ and $Y$, respectively. What is the minimum possible area of triangle $AXY$?

$\frac1{3\sqrt3}$
$\frac1{2\sqrt3}$
$\frac{\sqrt3}{12}$
$\frac{\sqrt3}{8}$
None of the above.