MathDB

6

Part of 2002 Taiwan National Olympiad

Problems(1)

simson's line

Source: 11-th Taiwanese Mathematical Olympiad 2002

1/23/2007
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.
geometrygeometric transformationdilationratioparallelogramEulergeometry unsolved