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Find the shape and symmetries of the two pieces of this cut cube.

Mean Geometrically

A and B are two points on a circle centre O. Tangents at A and B cut at C. CO cuts the circle at D. What is the relationship between areas of ADBO, ABO and ACBO?

Logosquares

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.

Rose

Age 16 to 18
Challenge Level
There are four cases to consider:
(a) the group containing only the identity transformation
(b) groups containing the identity and rotations
(c) groups containing the identity and reflections
(d) groups containing the identity, reflections and rotations.