MathDB
Problem 1 - Juniors

Source: 24-th Hellenic Mathematical Olympiad

April 16, 2007
geometryincentercircumcircleangle bisectorgeometry proposed

Problem Statement

In a triangle ABCABC with the incentre I,I, the angle bisector ADAD meets the circumcircle of triangle BICBIC at point N≠IN\neq I. a) Express the angles of △BCN\triangle BCN in terms of the angles of triangle ABCABC. b) Show that the circumcentre of triangle BICBIC is at the intersection of AIAI and the circumcentre of ABCABC.
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