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the squares that have $BC$ and $AD$ as diagonals also have a common vertex

Source: Moldova TST 2000

August 7, 2023

geometry

Problem Statement

Let

ABCD

be a convex quadrilateral. Two squares are constructed such that

AB{}

and

CD{}

are their diagonals. Show that if these squares have a common vertex inside

ABCD

, then the squares that have

BC{}

and

AD{}

as diagonals also have a common vertex inside

ABCD