10/06/05 MATHEMATICS DEPARTMENT, FERRIS STATE UNIVERSITY

MATH COLLOQUIUM, THURSDAY, OCTOBER 06, 11:00am, STARR 138

SPEAKER: Dr. Vaclav Konecny,

Mathematics Department, Ferris State University

TITLE: The solution to the problem published in Crux Mathematicorum, Vol. 30, No 7, November 2004, p. 429.

Dr. Konecny will present the solution to the problem proposed by Christopher J. Bradley, Bristol, UK (Crux Mathematicorum, Vol. 30, No 7, November 2004, p. 429.)

Let ABCD be a cyclic quadrilateral. The internal bisectors of angles A and B meet at P. Points Q, R, S are similarly defined by a cyclic change of letters. It is easy to show that PQRS is a cyclic quadrilateral. Suppose that the circles ABCD and PQRS have centers O and X, respectively. Let AC meet BD at E. Prove that O, E, and X are collinear. Prove also that .

REFRESHMENTS: 11:00 am, STARR 138

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