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About bicentric quadrilaterals

Source: Brazil Math Olympiad 1995

March 16, 2006
geometrycircumcirclerectangleperpendicular bisectorBrazilian Math Olympiad

Problem Statement

ABCDABCD is a quadrilateral with a circumcircle centre OO and an inscribed circle centre II. The diagonals intersect at SS. Show that if two of O,I,SO,I,S coincide, then it must be a square.
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