What a proposal

Geometry Level 5

In the figure below

the quadrilateral \(ABCD\) is inscribed in a circle. The lines \(AB\) and \(CD\) meet at \(E\).The diagonals \(AC\) and \(BD\) meet at \(F\). The circumcircles of the triangle \(AFD\) and \(BFC\) meet again at \(H\). Find the measure of angle \(EHF\) in degrees.

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