Geometric Probablity

An ellipse of eccentricity \(\frac { 2\sqrt { 2 } }{ 3 } \) is inscribed in a circle and a point is chosen at random. If the probability that this point lies outside the ellipse is expressed as \( \frac { a }{ b }\) where \(a,b\) are co-prime integers.

Now let the previous ellipse is made up of thin wire of total length \(L\) then if we cut this wire in 3 pieces. If the probability That these three pieces forms triangle is expressed as \(\frac { c }{ d } \) where \(c,d\) are co-prime integers.

Which of following options is correct?

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