MathDB
concurrent lines incenter

Source: Middle European Mathematical Olympiad I-3

September 20, 2014
geometryincentersymmetryangle bisectorperpendicular bisectorgeometry proposed

Problem Statement

Let ABCABC be a triangle with AB<ACAB < AC and incentre II. Let EE be the point on the side ACAC such that AE=ABAE = AB. Let GG be the point on the line EIEI such that ∠IBG=∠CBA\angle IBG = \angle CBA and such that EE and GG lie on opposite sides of II.
Prove that the line AIAI, the line perpendicular to AEAE at EE, and the bisector of the angle ∠BGI\angle BGI are concurrent.
Back to ProblemsView on AoPS