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?
Stage: 5 Challenge Level:
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.
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