A Black n' Pink Problem

Geometry Level 4

Here you see 3 identical circles of maximum area have so nicely been packed inside the ellipse along the major axis.

The circles have been painted black and the rest of the ellipse pink.

Find the value of the ratio A r e a i n B l a c k A r e a i n P i n k \frac{Area\;in\; Black}{Area\;in\;Pink} .

1.000 0.577 1.234 1.366 0.846

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