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Circle Passing Through a Fixed Point

Source: Azerbaijan IMO TST 2017, D2 P1

May 26, 2018
geometrycircumcircle

Problem Statement

Let ABCABC be an acute angled triangle. Points EE and FF are chosen on the sides ACAC and ABAB, respectively, such that BC2=BA×BF+CE×CA.BC^2=BA\times BF+CE\times CA. Prove that for all such EE and FF, circumcircle of the triangle AEFAEF passes through a fixed point different from AA.
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