# Balancing a Semicircle Frame

A semicircle with a constant mass per unit length is placed on a horizontal surface such that it doesn't topple in any direction. The touch point $$P$$ is assumed not to slip from the surface. Also, the imaginary line connecting the two end points of the semicircle forms an angle of $$\theta$$ with the surface.

Find the measure of $$\theta$$ (in degrees) to 2 decimal places.

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