Inscribing four semi circles that touch each other inside a circle. The method can be extrapolated to any number of semi circles.
Divide into n sectors
Find angle bisector of each sector (centres of semi circles must lie on this line)
At Circumference, measure 45 degrees from radius (can use angle bisector between radius and tangent). Add a construction line. where this meets a radius of an original sector must be where the semi circle meets that sector (Think about your GCSE circle theorems).
Draw a circle from the centre of the original circle that passes through this point in order to locate extremes of the diameter of each semi circle
Locate the mid point of each diameter in order to find the centres of each semi circle
Draw the semi circles and job done
This skill will be useful when constructing some tracery window designs
My daughter told me that she would only be interested in these designs if there was colour.
The construction above was done using free version of cabri-express, and then saving the picture into a paint document, in order to to be able to both delete all the construction lines and then use fill to add colour
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