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Thinking about Geometry

Review question

If a cone sits on this sphere, what 's the cone's volume?
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Ref: R9694

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Suggestion

A sphere of radius \(\quantity{6}{cm}\) fits inside a cone of vertical angle \(84^\circ\), so that \(BA\) is a tangent to the sphere.

The sphere and cone described in the question; the point $B$ is the apex of the cone and $A$ lies on the intersection between the sphere and the base circle of the cone.

Calculate

the length \(AB\);

Could we draw a sketch? Are there any triangles that could be useful? What happens when we add the information from the question to this diagram?