MathDB
Hungary-Israel Binational 1990_2

Source:

October 28, 2008
geometryparallelogramgeometric transformationrotationgeometry proposed

Problem Statement

Let ABC ABC be a triangle where \angle ACB\equal{}90^{\circ}. Let D D be the midpoint of BC BC and let E E, and F F be points on AC AC such that CF\equal{}FE\equal{}EA. The altitude from C C to the hypotenuse AB AB is CG CG, and the circumcentre of triangle AEG AEG is H H. Prove that the triangles ABC ABC and HDF HDF are similar.
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