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:

Prove that the area of a quadrilateral is given by half the
product of the lengths of the diagonals multiplied by the sine of
the angle between the diagonals.