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# Two circles on the Delta

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Posted 06 April 2013 - 03:38 AM

You have 2 different sized circles in a 2-dimensional plane. The smaller one is inside the larger with both centers at the same point C. The smaller circle can rotate while the larger circle is stationary.

There are 3 different types of points: Type X, Type A, Type B. There must be at least 3 X points at the circumference of the smaller circle, evenly spaced. Type A and B points are put at the circumference of the larger circle as follows. A and B must be placed as a pair, A before B in a clockwise fashion, given a distance Delta apart (not arch length, straight line distance). There must be at least 3 pairs of A and B, but they do not have to be evenly spaced. However, each pair must be at least Delta distance apart.

A CXA radius is defined as when an X point aligns with both point A and C (center) in which a line can be drawn to make a raduis of the larger circle. A CXB radius is defined as when an X point aligns with both point B and C (center) in which a line can be drawn to make a raduis of the larger circle.

The object is to place the X points evenly spaced on the smaller circle and the A-B pairs on the larger circle such that, during a 360 degree clockwise rotation of the smaller circle there are always more CXB radii than CXA radii at any point of the rotation. What is the minimum number of X points, minimum number of A-B pairs and their locations (in degrees), and the radius of the larger circle if:

Delta = .875"?

Delta = 2.25"?

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