MathDB
angle bisection

Source: Italy TST 2000

September 27, 2008
linear algebramatrixsymmetrygeometryangle bisectorgeometry unsolved

Problem Statement

Let ABC ABC be an isosceles right triangle and MM be the midpoint of its hypotenuse ABAB. Points DD and EE are taken on the legs ACAC and BCBC respectively such that AD=2DCAD=2DC and BE=2ECBE=2EC. Lines AEAE and DMDM intersect at FF. Show that FCFC bisects the ∠DFE\angle DFE.
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