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1950s Maths O level

RAQ is a tangent at A to the circle ABC. The lines BQ and CR are perpendicular to the tangent and AP is perpendicular to BC.

Show that: BQ/AP = AP/CR

Four interlocking wheels

I hope this is a well-defined question!

I'm interested in a general formula for the area shaded in blue as you roll four interlocking (perhaps geared) wheels as shown in the diagram above. Sounds like a nice advanced GCSE or O level question? Assume the wheels have the same radius r. What is the minimum and maximum of the shaded area?

This will stop me playing around with biscuits. Perhaps I need to buy some Meccano.

Su Doku solver

My Su Doku solver is here for you to try.

It does not just present you with the solution but rather it leads you through solving it yourself by suggesting numbers for each square for which it has determined there is a unique answer.  As set up it has a default puzzle but you can change any and all of the numbers to start the solution of your own puzzles.  Give it a go!  It is a useful aid to teaching and having “maths fun” – or should I say logic?

You do not need a logon to download the file and save it as your own copy.  Note however that in Internet Explorer (because of a known problem with its interface to sites such as this one) you may see a request to provide an ID and password.  Press cancel, perhaps twice, and it will open the file quite happily.  If you are using firefox or chrome you will not get this problem.