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Bulgaria National Olympiad

Source: Bulgaria National Olympiad, Fourth round, P5

March 21, 2021
geometrycircumcircleBulgaria

Problem Statement

The quadrilateral ABCDABCD is inscribed in a circle. The lines ABAB and CDCD meet each other in the point EE, while the diagonals ACAC and BDBD in the point FF. The circumcircles of the triangles AFDAFD and BFCBFC have a second common point, which is denoted by HH. Prove that ∠EHF=90∘\angle EHF=90^\circ.
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