A small circle fits between two touching circles so that all three
circles touch each other and have a common tangent? What is the
exact radius of the smallest circle?
Two semicircle sit on the diameter of a semicircle centre O of
twice their radius. Lines through O divide the perimeter into two
parts. What can you say about the lengths of these two parts?
Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?
The circles centres $O$, $A$, $B$ and $C$ touch one another.
Prove that the radii of the circles with centres $A$, $B$ and $C$
are in the ratio $1 : 2 : 3$ and that the triangles $OBC$ and $ABC$
are right angled $3 : 4 : 5$ triangles.