Sine, cosine, tangent

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Favourite

Logosquares

Age

16 to 18

Challenge level

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.
problem
Favourite

Three by One

Age

16 to 18

Challenge level

There are many different methods to solve this geometrical problem - how many can you find?
problem
Favourite

Belt

Age

16 to 18

Challenge level

A belt of thin wire, length L, binds together two cylindrical welding rods, whose radii are R and r, by passing all the way around them both. Find L in terms of R and r.
problem
Favourite

Shape and Territory

Age

16 to 18

Challenge level

If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?
problem
Favourite

So Big

Age

16 to 18

Challenge level

One side of a triangle is divided into segments of length a and b by the inscribed circle, with radius r. Prove that the area is: abr(a+b)/ab-r^2
problem

Coke Machine

Age

14 to 16

Challenge level

The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
problem

30-60-90 Polypuzzle

Age

16 to 18

Challenge level

Re-arrange the pieces of the puzzle to form a rectangle and then to form an equilateral triangle. Calculate the angles and lengths.
problem

Sine Problem

Age

16 to 18

Challenge level

In this 'mesh' of sine graphs, one of the graphs is the graph of the sine function. Find the equations of the other graphs to reproduce the pattern.
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Farhan's Poor Square

Age

14 to 16

Challenge level

From the measurements and the clue given find the area of the square that is not covered by the triangle and the circle.
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Small Steps

Age

16 to 18

Challenge level

Two problems about infinite processes where smaller and smaller steps are taken and you have to discover what happens in the limit.