Diagram above shows a circle with center \(D\), with \(C,E,F\) be points lying on the circle, and two right triangles \(ACD\) and \(BCE\) with their hypotenuse intersect at \(F\). If we are given \(AC = CD = 10 \text{ cm} \). What is the area of triangle \(ABF \) to 4 decimal places.

**Details and Assumptions**

- You may use the approximation: \( \sqrt 2 = 1.41421356 \)

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