Construct tangents at P and Q meeting at T.
Draw a circle with diameter OT.
Do P and Q lie inside, or on, or outside this circle?
Explain your answer.

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Now imagine a sphere with diameter OT.
Do P and Q lie inside, or on, or outside this sphere?
Explain your answer. You may find an interactive hint in the second iteractive problem:

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If you can see the diagrams above, try clicking and dragging the red points.

To experiment further with this problem, download a copy of Geometer's Sketch Pad.