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.

## Monday, July 27, 2015

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

Labels:
circle,
circumcircle,
collinear,
line,
reflection,
tangent,
triangle

Subscribe to:
Post Comments (Atom)

Partial solution:

ReplyDeleteLet 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

This problem is the same as problem number 6 of International Mathematic Olympiad 2011

ReplyDeleteSee 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