Challenge Level

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:

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