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danube junior angle chasing 2018 P2

Source: Danube Junior 2018 P2

December 11, 2018
geometryAngle Chasingperpendicularperpendicularity

Problem Statement

Let ABCABC be a triangle such that in its interior there exists a point DD with ∠DAC=∠DCA=30o\angle DAC = \angle DCA = 30^o and ∠DBA=60o \angle DBA = 60^o. Denote EE the midpoint of the segment BCBC, and take FF on the segment ACAC so that AF=2FCAF = 2FC. Prove that DE⊥EFDE \perp EF.
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