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Find all possible values of angle A

Source: USAMO 1987 Problem 2

July 24, 2011
geometry unsolvedgeometry

Problem Statement

ADAD, BEBE, and CFCF are the bisectors of the interior angles of triangle ABCABC, with DD, EE, and FF lying on the perimeter. If angle EDFEDF is 9090 degrees, determine all possible values of angle BACBAC.
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