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Geometry Level 5

The white ring, blue small circle, and tri-colored big circle are all cocentric at point O. Point A is moving around the circumference of the small blue circle and point B is moving around the circumference of the large circle at a different angular velocity. When O, A, and B are co-linear, segment \(\overline{AB}\) has a length of 4. When the measure of \(\angle{OAB}=90\) (\(\overline{AB}\) is tangent to the smaller circle), segment\(\overline{AB}\) has a length of 8. Point P is stationary at an arbitrary position on the outside circumference of the white ring. If the minimal distance between points A and P is 1, find the area of the yellow sector.

Assume:

The yellow, blue, and green sectors are congruent.

Points P,A,B stay on their respective circumferences.

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