An Exercise in Solid Angle Computation

Geometry Level 5

A pentagon lies in the XY plane centered at the origin. The pentagon is inscribed within a circle of radius equal to \( 5 \) units. Point A lies on the z-axis, \( 10 \) units from the center of the pentagon. If the solid angle subtended by the pentagon at the point A is given by \( x \pi \), what is \( x \) , correct to 3 decimal places ?

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