Definitions for osculating circle
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Princeton's WordNet
circle of curvature, osculating circle(noun)
the circle that touches a curve (on the concave side) and whose radius is the radius of curvature
Wiktionary
osculating circle(Noun)
The circle that has the same tangent, and the same curvature at the point on the curve
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"osculating circle." Definitions.net. STANDS4 LLC, 2013. Web. 23 May 2013. <http://www.definitions.net/definition/osculating circle>.