All These Chords

Geometry Level 3

Suppose we have a circle \(O\) and a point \(P\) such that point \(P\) is inside circle \(O\). Furthermore, the radius of circle \(O\) is \(20\), and the shortest distance from \(P\) to the circumference of the circle is \(8\). How many distinct chords can be drawn such that it has an integer length and passes through point \(P\)?

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