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JBMO TST 2020 - Moldova P11

Source: JBMO TST 2020 Moldova

October 13, 2020
geometrycircumcircle

Problem Statement

Let △ABC\triangle ABC be an acute triangle. The bisector of ∠ACB\angle ACB intersects side ABAB in DD. The circumcircle of triangle ADCADC intersects side BCBC in CC and EE with C≠EC \neq E. The line parallel to AEAE which passes through BB intersects line CDCD in FF. Prove that the triangle △AFB\triangle AFB is isosceles.
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