Ten squares form regular rings either with adjacent or opposite
vertices touching. Calculate the inner and outer radii of the rings
that surround the squares.
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.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice.