Quote Originally Posted by p45cal View Post
As far as I can tell, the larger half circle size is determined by the quadrant radius - nothing else.
The smaller half circle , if it's to fit by just touching the larger half circle and its top being at the top of the vertical leg of the quadrant, has a diameter about (exactly?) 2/3rds the diameter of the larger half circle. So the linear proportions remain the same regardless of scale, so all areas are in proportion to the square of the linear dimensions.
The function I gave gives the same results as your calculations; have you compared?
For the purpose of this exercise then yes it just happens that the bigger half circle is half the size of the radius of the quadrant. Done the track it may not. In fact I envisage that either the Quadrant or the half circles may differ in dimensions from those supplied in the graphic.