# Intersecting Chords

Geometry Level 4

Shown in the figure above is circle $$O$$ with radius 6 inches. Chord $$CD$$ is drawn perpendicular to radius $$AO$$ so that its midpoint is 3 inches from the center of the circle. From point $$A$$, any chord $$AB$$ is drawn intersecting $$CD$$ at point $$M$$. Let $$v$$ be equal to the product $$(AB)(AM)$$, as chord $$AB$$ is made to rotate in the circle about the fixed point $$A$$. Find $$v$$.

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