Determine the least real number $a > 1$ such that for any point $P$ in the interior of a square $ABCD$, the ratio of the areas of some two triangle $PAB, PBC, PCD, PDA$ lies in the interval $[1/a, a]$.
Source: Indian Postal Coaching 2009 set 2 p4
Tags: areas, square, geometry
Determine the least real number $a > 1$ such that for any point $P$ in the interior of a square $ABCD$, the ratio of the areas of some two triangle $PAB, PBC, PCD, PDA$ lies in the interval $[1/a, a]$.