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ratio of areas of some 2 triangle PAB, PBC, PCD, PDA$ lies in interval [1/a, a]

Source: Indian Postal Coaching 2009 set 2 p4

May 26, 2020
areassquaregeometry

Problem Statement

Determine the least real number a>1a > 1 such that for any point PP in the interior of a square ABCDABCD, the ratio of the areas of some two triangle PAB,PBC,PCD,PDAPAB, PBC, PCD, PDA lies in the interval [1/a,a][1/a, a].
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