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## 'Three Balls' printed from http://nrich.maths.org/

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 .