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computational inside a 80-80-20 triangle, BC=12, ABE= 30^o , EF = FC

Source: December 2020 Ukraine Geometry Olympiad VIII p4

December 21, 2020
geometryisoscelesanglesequal segments

Problem Statement

In an isosceles triangle ABCABC with an angle ∠A=20o\angle A= 20^o and base BC=12BC=12 point EE on the side ACAC is chosen such that ∠ABE=30o\angle ABE= 30^o , and point FF on the side ABAB such that EF=FCEF = FC . Find the length of FCFC.
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