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High school mathematics solid geometry problem: how to determine the circumscribed sphere radius of regular triangular prism?
Solution: let the side length of the bottom surface be a and the height be h.

Then the center of catching the ball is on the connecting line PP 1 between the centers of the two soles, and the center O is the midpoint of PP 1.

Radius r = OA = √ (op 2+pa 2)

=√((h/2)^2+(√3a/3)^2)

=√(h^2/4+a^2/3)