A circle has centre O and $\angle \mathrm{POR}=\angle \mathrm{QOR}.$

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.

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:

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