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.

If a is the radius of the axle, b the radius of each ball-bearing, and c the radius of the hub, why does the number of ball bearings n determine the ratio c/a? Find a formula for c/a in terms of n.

Diagonals for Area

Age 16 to 18 Challenge Level:

This only uses the result that the area of a triangle is half
the base times the height but you need to consider different cases
according to whether the quadrilateral is convex or concave.