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find the range of angle BAC

Source: China TST 1989, problem 6; China North MO

June 27, 2005
trigonometrygeometryfunctionangle bisectorgeometry solved

Problem Statement

ADAD is the altitude on side BCBC of triangle ABCABC. If BC+AD−AB−AC=0BC+AD-AB-AC = 0, find the range of ∠BAC\angle BAC. Alternative formulation. Let ADAD be the altitude of triangle ABCABC to the side BCBC. If BC+AD=AB+ACBC+AD=AB+AC, then find the range of ∠A\angle{A}.
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