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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