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Three circles for equal lenghts

Source: Germany 2011, Grade 13 - #3

May 29, 2016
geometrycircumcirclegeometry unsolvedaltitudeorthic triangle

Problem Statement

Let ABCABC be an acute triangle and DD the foot of the altitude from AA onto BCBC. A semicircle with diameter BCBC intersects segments AB,ACAB,AC and ADAD in the points F,EF,E resp. XX. The circumcircles of the triangles DEXDEX and DXFDXF intersect BCBC in LL resp. NN other than DD. Prove BN=LCBN=LC.
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