201. Reflections of a Point on the Circumcircle

Reflections of a point on the circumcircle in the sidelines of a triangle are collinear with the orthocenter of the triangle
URL: http://www.cut-the-knot.org/Curriculum/Geometry/ThroughOrthocenter.shtml - 25kb - 19 Jun 2006

202. Five Incircles Theorem

Five Incircles Theorem: 2 cevians from the apex of a triangle split into 3 smaller triangles of level 1. Combined by 2 they form 2 triangles of level 2, etc. The ncircles of the first and third triangle of level 1 are equal iff the incircles of the two second level triangles are also equal
URL: http://www.cut-the-knot.org/Curriculum/Geometry/FourIncircles.shtml - 25kb - 19 Jun 2006

203. Pedal Polygons

Pedal Polygons: for a point on the circumcircle of an inscribed polygon, draw the slants equally inclined to each of the lines through the center of the circle and its vertices. The resulting polygon does not depend on the position of the point on the circle.
URL: http://www.cut-the-knot.org/Curriculum/Geometry/ProjectedPoly.shtml - 25kb - 19 Jun 2006

204. Thébault's Problem III

Thébault's Problem III: centers of two circles that touch the base of a triangle, its circumcenter and a cevian are collinear
URL: http://www.cut-the-knot.org/Curriculum/Geometry/Thebault3.shtml - 25kb - 19 Jun 2006

205. Thébault's Problem I

Thébault's Problem I: the centers of squares erected on the sides of a parallelogram form a square.
URL: http://www.cut-the-knot.org/Curriculum/Geometry/Thebault1.shtml - 25kb - 19 Jun 2006

206. Bottema's Theorem

Bottema's Theorem
URL: http://www.cut-the-knot.org/Curriculum/Geometry/Bottema.shtml - 25kb - 19 Jun 2006

207. Reflections of the Orthocenter

Reflections of the Orthocenter in the sidelines of a triangle lie on the circumcircle of the latter
URL: http://www.cut-the-knot.org/Curriculum/Geometry/AltitudeAndCircumcircle.shtml - 25kb - 19 Jun 2006

208. Similar Triangles on Sides of a Quadrilateral

Similar Triangles on Sides of a Quadrilateral: if similar triangles are erected on the sides of an quadrilateral in a certain way, a parallelogram emerges
URL: http://www.cut-the-knot.org/Curriculum/Geometry/deVilliers.shtml - 25kb - 19 Jun 2006

209. A Property of Equiangular Polygons

A Property of Equiangular Polygons: the sum of distances of from a point to the sides of an equiangular polygon is invariant of a polygon
URL: http://www.cut-the-knot.org/Curriculum/Geometry/EquiangularPoly.shtml - 25kb - 19 Jun 2006

210. Gergonne and Medial Triangles Are Orthologic

Gergonne and Medial Triangles Are Orthologic
URL: http://www.cut-the-knot.org/Curriculum/Geometry/GergonneMedial.shtml - 25kb - 19 Jun 2006

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