finding relationships between the radii, between a radius and the side length of a square (first sheet) or the length of an equilateral triangle (third sheet) can and probably ought to involve:
- symmetry
- exact trigonometric values
- surd manipulation
the first sheet doesn't need trigonometry, just pythagoras in an isosceles right angled triangle
you do not need to manipulate surds, but you obtain simpler looking solutions if you do
the second sheet involves expanding brackets and some not too hefty algebra, to obtain a neat result
the third sheet involves exact trigonometric values for 30 and 60 degree angles
well, I think they are anyway...
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