MathDB
Parallel lines

Source: Korea National 2012 Problem 6

August 19, 2012
geometryratiogeometric transformationdilationreflectiongeometry proposed

Problem Statement

Let w w be the incircle of triangle ABC ABC . Segments BC,CA BC, CA meet with w w at points D,E D, E. A line passing through B B and parallel to DE DE meets w w at F F and G G . (F F is nearer to B B than G G .) Line CG CG meets w w at H(≠G) H ( \ne G ) . A line passing through G G and parallel to EH EH meets with line AC AC at I I . Line IF IF meets with circle w w at J(≠F) J (\ne F ) . Lines CJ CJ and EG EG meets at K K . Let l l be the line passing through K K and parallel to JD JD . Prove that l,IF,ED l, IF, ED meet at one point.
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