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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