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Degree Ceremony

Can you find the sum of the squared sine values?


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.

Ball Bearings

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.

Geometric Trig

Age 16 to 18 Short
Challenge Level

This problem uses basic notions of trigonometry and areas of triangles which are fundamental to developments in A-level mathematics.
Being able to work with diagrams such as this is useful prepation for both coordinate geometry and mechanics.