Circle gets cozy in triangle

Geometry Level 3

In \(\triangle{\text{ABC}}\), \(\text{AD}\), \(\text{BD}\) and \(\text{CD}\) are the bisectors of \(\angle{\text{BAC}}\), \(\angle{\text{ABC}}\) and \(\angle{\text{ACB}}\) respectively.
If \(\text{AFDE}\) is a rectangle such that \(\text{AD} = \text{10 cm}\) and \(\text{AE} = \text{8 cm}\), find the area of the circle inscribed in \(\triangle{\text{ABC}}\).

Round your answer( in \({\text{cm}}^{2}\)) to the nearest integer.

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