Monday, July 27, 2015

Geometry Problem 1143: Triangle, Circumcircle, Tangent Line, Reflection of a Point over a Line, Tangent Circles, Collinear Points

Geometry Problem. Post your solution in the comments box below.
Level: Mathematics Education, High School, Honors Geometry, College.

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Online Math: Geometry Problem 1143: Triangle, Circumcircle, Tangent Line, Reflection of a Point over a Line, Tangent Circles, Collinear Points.

Posted by Antonio Gutierrez at 4:45 PM
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2 comments:

  1. Peter TranJuly 28, 2015 at 12:43 PM

    Partial solution:
    Let B0, C0 and A0 are the projection of T over AC, AB and BC
    Since A0B0C0 is the Simpson line of point T so A0, B0 and C0 are collinear
    We have TB2/TB0=TA2/TA0=TC2/TC0= 2 so A2, B2 and C2 are collinear

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  2. Peter TranJuly 28, 2015 at 5:34 PM

    This problem is the same as problem number 6 of International Mathematic Olympiad 2011
    See links below for problem and different solutions using Inversion or Angles chasing or complex numbers
    http://s27.postimg.org/jl1t2owjn/pro_1143_or_IMO2011_6.png
    http://www.artofproblemsolving.com/community/c6h418983p2365045

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