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equal angles wanted and given, angle bisector and right angle related

Source: 2001 Argentina OMA L3 p2

June 15, 2020
geometryangle bisectorequal anglesangles

Problem Statement

Let △ABC\vartriangle ABC be a triangle such that angle ∠ABC\angle ABC is less than angle ∠ACB\angle ACB. The bisector of angle ∠BAC\angle BAC cuts side BCBC at DD. Let EE be on side ABAB such that ∠EDB=90o\angle EDB = 90^o and FF on side ACAC such that ∠BED=∠DEF\angle BED = \angle DEF. Prove that ∠BAD=∠FDC\angle BAD = \angle FDC.
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