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A hypocycloid degenerates into a straight line when the rolling circle's diameter is

  • A.one tenth that of the directing circle
  • B.half that of the directing circle
  • C.equal to that of the directing circle
  • D.twice that of the directing circle

Answer: B

With the radius ratio at one half, the tracing point sweeps back and forth along a diameter of the fixed circle instead of describing arches. A quarter ratio gives four cusps and the astroid rather than a straight line.

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