Geo-math-trick (Geometry)!

Geometry Level 5

If $$\triangle ABC$$ and $$\triangle ADC$$ are Right angled triangle with$$\angle DCA=\angle BAC=90^{\circ}$$ with $$AC$$ being the smallest side for each triangle and both the circles have equal diameter of $$68$$ cm. And each side of both the triangles is an integer.

Then find the minimum area of the blue region in $$\text{cm}^{2}$$. Correct your answer to three decimal places before entering it.

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