circles with different radius and center
- Author:
- chris cambré
- With the green point M=O we get a semicircle.
- If we drag M rightwards on the segment AB, we get a pointed arch.
- With P as a point on the segment AB construct a circle with radius AP and center P.
- Draw the line MP and create the intersection point N with the circle.
- Now create the circular arc AN with center P and the circular arc NO' with center M.
The mathematical logic of this construction with different curvatures is simple.
3 points have to be collinear: the transition point of the two circular arcs and their two centers.
Because if so:
- The radii of the two cricular arcs may be different, but their direction is coinciding.
- The tangent of a circle in a point on that circle is perpendicular to the radius.
- conclusion: the tangents in point N of the two parts are the same and thus their transition is smooth.