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<BAC=? DE = BC, lines altitudes intersect circumcircle

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2015 3.1

September 23, 2021
anglesgeometrycircumcircle

Problem Statement

Let △ABC\vartriangle ABC be such that ∠BAC\angle BAC is acute. The line perpendicular on side ABAB from CC and the line perpendicular on ACAC from BB intersect the circumscribed circle of △ABC\vartriangle ABC at DD and EE respectively. If DE=BCDE = BC , calculate ∠BAC\angle BAC.
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