Problems with everyday objects: the tear drop

Geometry Level 5

Keeping its beauty in mind, find the area (A) you may try.

Input your answer as \(\lfloor 100A \rfloor \) where \(\lfloor x \rfloor \) is the greatest integer function (the greatest integer less than or equal to x).


\(~~~~ \) Assume:

The red curve is defined by the function \(x^2+(y-20+10\sqrt3)^2=(10\sqrt3-15)^2\)

The blue curve is defined by the function \((x-10\sqrt3+15)^2+(y+10-5\sqrt3)^2=(10\sqrt3-15)^2\)

The green curve is defined by the function \(x^2+y^2=25\).

The blue curve ends at its point of tangency with the red curve and green curve

Each curve begins and ends at a point of tangency.

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