Projected Incircle

Geometry Level 5

A plane \(a\) has an equation: \[\frac{x}{3} + \frac{y}{4} + \frac{z}{5}=1\] A triangle has as its vertices points of intersection of the plane \(a\) with the axes of the coordinate system. Incircle of that triangle is projected onto the \(XY\) plane and the projected shape has an area \(A\). Give answer as \[\lfloor A \times 10000 \rfloor\]

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