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I kind of love this stuff and had some relevant code laying around, so... The kite-domino tiling is based the pinwheel tiling which is falls out of a particular decomposition of a right triangle with legs of length 1 and 2. In the code that follows, rt[{a,b,c}] represents such a right triangle and dissect indicates how such a triangle should be decomposed ...


This is an extended version of the brief suggestion that I gave in my comment above. Solve for the tangent points. Solve[{#.# &[{x1, y1} - {0, 0}] == 3^2, #.# &[{x2, y2} - {12, 0}] == 2^2, (y2 - y1)/(x2 - x1) == -((x1 - 0)/(y1 - 0)) == -((x2 - 12)/(y2 - 0))}, {x1, y1, x2, y2}] (* This gives 4 solutions *) Define the extrusion vector. ...


For the first question the problem is only in the radius of the small circle. it should be like this: Circle[center[{R, r}, θ], r]

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