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

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:


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 .