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a B,I,G problem

Source: Italy TST 2003

November 9, 2010
geometrygreatest common divisorcircumcirclegeometry unsolved

Problem Statement

The incircle of a triangle ABCABC touches the sides AB,BC,CAAB,BC,CA at points D,E,FD,E,F respectively. The line through AA parallel to DFDF meets the line through CC parallel to EFEF at GG. (a)(a) Prove that the quadrilateral AICGAICG is cyclic. (b)(b) Prove that the points B,I,GB,I,G are collinear.
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