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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