221. Nagel Line

Nagel Line: incenter, centroid, Nagel point and Spieker Center are collinear
URL: http://www.cut-the-knot.org/Curriculum/Geometry/NagelLine.shtml - 26kb - 19 Jun 2006

222. Fixed Point of Circles Orthogonal to the Given One

Fixed Point of Circles Orthogonal to the Given One
URL: http://www.cut-the-knot.org/Curriculum/Geometry/FixedTangentPoint.shtml - 26kb - 19 Jun 2006

223. Touching Circles With Given Centers

Touching Circles With Given Centers: for an odd number of points there always exist pairwise touching circles with centers at those points. The problem is shown to be equivalent to an absolutely different one.
URL: http://www.cut-the-knot.org/Curriculum/Geometry/TouchingCircles.shtml - 26kb - 19 Jun 2006

224. Pole and Polar wrt a Triangle

Pole and Polar with respect to a Triangle
URL: http://www.cut-the-knot.org/Curriculum/Geometry/PolePolarTriangle.shtml - 26kb - 19 Jun 2006

225. Polar Circle

Polar Circle: curcumcircle and 9-point circle are inverse images of each other in the polar circle
URL: http://www.cut-the-knot.org/Curriculum/Geometry/PolarCircle.shtml - 26kb - 19 Jun 2006

226. Perpendicular Bisectors in an Inscriptible Quadrilateral

Perpendicular Bisectors in an Inscriptible Quadrilateral form another inscripible quadrilateral
URL: http://www.cut-the-knot.org/Curriculum/Geometry/deVilliers2.shtml - 27kb - 19 Jun 2006

227. Circles On Cevians

Circles On Cevians: the radical center of three circles built on any three Cevians as diameters coincides with the orthocenter of the triangle
URL: http://www.cut-the-knot.org/Curriculum/Geometry/CircleOnCevian.shtml - 27kb - 19 Jun 2006

228. Property of Points Where In- and Excircles Touch a Triangle

Property of Points Where In- and Excircles Touch a Triangle
URL: http://www.cut-the-knot.org/Curriculum/Geometry/TouchPoint.shtml - 27kb - 19 Jun 2006

229. Newton's Theorem and Leon Anne's Theorem

Newton's Theorem and Leon Anne's Theorem
URL: http://www.cut-the-knot.org/Curriculum/Geometry/NewtonTheorem.shtml - 27kb - 19 Jun 2006

230. Inversion in the Incircle

Inversion in the Incircle: inversion of the side lines of a triangle in its incircle generates three equal circles through the incenter. The circle through their other points of intersection is the inverse image of the circumcircle
URL: http://www.cut-the-knot.org/Curriculum/Geometry/ThreeEqualCircles.shtml - 27kb - 19 Jun 2006

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