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simson's line

Source: 11-th Taiwanese Mathematical Olympiad 2002

January 23, 2007
geometrygeometric transformationdilationratioparallelogramEulergeometry unsolved

Problem Statement

Let A,B,CA,B,C be fixed points in the plane , and DD be a variable point on the circle ABCABC, distinct from A,B,CA,B,C . Let IA,IB,IC,IDI_{A},I_{B},I_{C},I_{D} be the Simson lines of A,B,C,DA,B,C,D with respect to triangles BCD,ACD,ABD,ABCBCD,ACD,ABD,ABC respectively. Find the locus of the intersection points of the four lines IA,IB,IC,IDI_{A},I_{B},I_{C},I_{D} when point DD varies.
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