# When parabola meets a rectangle

Geometry Level 4

The figure shows a rectangle $$ABCD$$ with $$C(0,0)$$,$$AC=4$$,$$AB=8$$.Point $$O$$ is the centre of gravity,and curves $$AOB,BOC,COD,AOD$$ are parabolas passing through it. Line $$PQ$$ is perpendicular to $$OD$$ and passes through the mid-point of $$OD$$. What is the length of $$PQ$$? Give your answer corrected to 3 sig.fig.

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