Mad Mirrors

Geometry Level 5

Two mirrors (represented by line segments in the plane) each have length 1 meter. They are joined such that one endpoint of one mirror coincides with one endpoint of the other mirror at the point \(A\) and such that the angle between the mirrors is 1 degree. Let points \(B\) and \(C\) be the remaining two endpoints which are not joined. A light source that emits light in all directions is placed at point \(P\) within triangle \(ABC\). Find the maximum number of times a light ray can bounce off of \(AB\) and/or \(AC\) before intersecting \(BC\). (For example, one such light ray can bounce off of \(AB\), then \(AC\), then \(AB\) again, then \(AC\) again, then \(AB\) again, and touch \(BC\); this light ray would have bounced off of \(AB\) and/or \(AC\) 5 times.)

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