MathDB

2

Part of 2009 Mediterranean Mathematics Olympiad

Problems(1)

Prove that 4 Points are Collinear

Source: 2009 MMO Problem #2

9/12/2011
Let ABCABC be a triangle with 90∘≠∠A≠135∘90^\circ \ne \angle A \ne 135^\circ. Let DD and EE be external points to the triangle ABCABC such that DABDAB and EACEAC are isoscele triangles with right angles at DD and EE. Let F=BE∩CDF = BE \cap CD, and let MM and NN be the midpoints of BCBC and DEDE, respectively.
Prove that, if three of the points AA, FF, MM, NN are collinear, then all four are collinear.
geometrycircumcirclegeometric transformationrotationgeometry unsolved