MathDB

1

Part of 2007 Greece Junior Math Olympiad

Problems(1)

Problem 1 - Juniors

Source: 24-th Hellenic Mathematical Olympiad

4/16/2007
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.
geometryincentercircumcircleangle bisectorgeometry proposed