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Geometry Problem. Post your solution in the comments box below.Level: Mathematics Education, High School, Honors Geometry, College.Click the diagram below to enlarge it.
Partial solution:Let B0, C0 and A0 are the projection of T over AC, AB and BCSince A0B0C0 is the Simpson line of point T so A0, B0 and C0 are collinearWe have TB2/TB0=TA2/TA0=TC2/TC0= 2 so A2, B2 and C2 are collinear
This problem is the same as problem number 6 of International Mathematic Olympiad 2011See links below for problem and different solutions using Inversion or Angles chasing or complex numbershttp://s27.postimg.org/jl1t2owjn/pro_1143_or_IMO2011_6.pnghttp://www.artofproblemsolving.com/community/c6h418983p2365045