# 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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