10/06/05 MATHEMATICS
DEPARTMENT, FERRIS STATE UNIVERSITY

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

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**SPEAKER: **Dr. Vaclav Konecny,

Mathematics Department, Ferris State University** **

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**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
_{}.

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**REFRESHMENTS: **11:00
am, STARR 138

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### Please visit Math Colloquium website at

http://www.ferris.edu/htmls/colleges/artsands/Math/MATH_COLLOQUIUM/ColloquiumWeb/index.html

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