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Rhombus and 2 circles

Source: Latvian TST for Baltic Way 2020 P12

October 18, 2020
geometryrhombus

Problem Statement

There are rhombus ABCDABCD and circle ΓB\Gamma_B, which is centred at BB and has radius BCBC, and circle ΓC\Gamma_C, which is centred at CC and has radius BCBC. Circles ΓB\Gamma_B and ΓC\Gamma_C intersect at point EE. The line EDED intersects ΓB\Gamma_B at point FF. Find all possible values of ∠AFB\angle AFB.
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