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<ABC wanted, EF bisects <AFD and <ADC = 80^o, circle

Source: 2001 Swedish Mathematical Competition p4

March 21, 2021
geometryangles

Problem Statement

ABCABC is a triangle. A circle through AA touches the side BCBC at DD and intersects the sides ABAB and ACAC again at E,FE, F respectively. EFEF bisects ∠AFD\angle AFD and ∠ADC=80o\angle ADC = 80^o. Find ∠ABC\angle ABC.
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