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# Retracircles

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Age 16 to 18

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.