Problem:
The circular base of a hemisphere of radius 2 rests on the base of a square pyramid of height 6 . The hemisphere is tangent to the other four faces of the pyramid. What is the edge-length of the base of the pyramid?
Answer Choices:
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Solution:
A cross section of the figure is shown, where is the apex, is the center of the base, and are the midpoints of opposite sides of the base, and the hemisphere meets at .
Right triangle has and , so . Because , it follows that
Hence the length of the base edge is .
The problems on this page are the property of the MAA's American Mathematics Competitions