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ABCD is a cyclic quadrilateral

Source: IMO LongList 1988, Mongolia 2, Problem 52 of ILL

November 3, 2005

geometrygeometric transformationreflectiongeometry unsolved

Problem Statement

ABCD

is a quadrilateral.

A'BCD'

is the reflection of

ABCD

BC,

A''B'CD'

is the reflection of

A'BCD'

CD'

and

A''B''C'D'

is the reflection of

A''B'CD'

D'A''.

Show that; if the lines

AA''

and

BB''

are parallel, then ABCD is a cyclic quadrilateral.