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equal angles after reflecting an external bisector on 2 internal bisectors

Source: IMAR 2012 p3

September 26, 2018
equal anglesgeometryreflectionangle bisector

Problem Statement

Given a triangle ABCABC, let DD be a point different from AA on the external bisectrix \ell of the angle BACBAC, and let EE be an interior point of the segment ADAD. Reflect \ell in the internal bisectrices of the angles BDCBDC and BECBEC to obtain two lines that meet at some point FF. Show that the angles ABDABD and EBFEBF are congruent.