this is based on an OCR, GCSE question:
in a similar vein:
this is from 'mental gymnastics' by dick hess
this is from an article by DP Eperson [in Mathematics in School, January 1992]
a square has touching circles, semicircles, quadrants drawn inside them:
intended to be practice in calculating areas of circles and bits of circles
[although several of the designs can be viewed as a scaling up, or down, of a part of another diagram]
this is from a John Mason session:
but solutions to how to find the area of overlap are found here
this next question requires an understanding of similar triangles:
[from a problem by Peter Grabarchuk here]
this is one of Paul Lockhart's problems (in 'measurement')
I think pythagoras is needed
the orange area is slightly bigger than the circle radius R
(square root 2) - 1
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