None of My Business?

Geometry Level 4

As shown in the diagram above, \(EA\), \(AB\), \(BC\) are chords in a circle so that \(EA\) is parallel to \(BC\).
\(O\) is the midpoint of \(AB\), \(P\) is the midpoint of \(BC\).
Chord \(AG\) passes through \(P\), and chord \(CD\) passes through \(O\).
Chord \(CD\) passes through \(O\), and intersects \(AG\) at \(N\).
Chord \(EF\) passes through \(O\), and intersects \(AG\) at \(M\).

If the area of \(\triangle AMO\) is 15 units and that of \(\triangle NOM\) is 10 units.
Find the diameter of the circle given that it is an integer.

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