solved
Hello, xMichaelx!
A Cone has a slant height and a semi-vertical angle
Prove that the radius of the inscribed sphere is given by:
. .
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The side view of the cone is
P is the center of the inscribed sphere: .
Note that
In right triangle
. . Hence: . .[1]
In right triangle .[2]
Equate [1] and [2]: .
Therefore: .