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Prove that the points L,E,F are collinear (5)

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October 28, 2010
geometrycircumcirclegeometric transformationdilationgeometry proposed

Problem Statement

A point EE lies on the altitude BDBD of triangle ABCABC, and ∠AEC=90∘.\angle AEC=90^\circ. Points O1O_1 and O2O_2 are the circumcenters of triangles AEBAEB and CEBCEB; points F,LF, L are the midpoints of the segments ACAC and O1O2.O_1O_2. Prove that the points L,E,FL,E,F are collinear.
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