Mysterious Angle Relation

Geometry Level 5

Let \(ABCD\) be a trapezoid with \(AB\parallel DC\) such that \(\angle DAC=50^{\circ}, \angle DBC=60^{\circ}\). Suppose \(AC\cap DB=E\), then denote \(G,F\) the projections from \(E\) onto \(AD,BC\), \(M\) is the midpoint of \(GF\).

If \(O\) is the circumcenter of \(\triangle DEC\), find \(\angle MEO\) in degrees.

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