81. The Law of Cosines

The Law of Cosines
URL: http://www.cut-the-knot.org/Curriculum/Geometry/CosineLaw.shtml - 23kb - 19 Jun 2006

82. Optimization Problem in Acute Angle

Optimization Problem in Acute Angle: A point A is given inside an acute angle. Find points B and C on the sides of the angle such that the perimeter of ABC is minimal
URL: http://www.cut-the-knot.org/Curriculum/Geometry/ProblemWithReflections.shtml - 23kb - 19 Jun 2006

83. Eight Point Circle

In a quadrilateral with orthogonal diagonals some 8 points lie on a circle
URL: http://www.cut-the-knot.org/Curriculum/Geometry/EightPointCircle.shtml - 23kb - 19 Jun 2006

84. Four Circles In a Triangle

Four Circles In a Triangle: cevians from the apex of a triangle split into smaller triangles of level 1. Combined by 2 they form triangles of level 2, etc. If incircles of all level 1 triangles are equal, the same holds for all higher levels
URL: http://www.cut-the-knot.org/Curriculum/Geometry/FourCirclesInTriangle.shtml - 23kb - 19 Jun 2006

85. A Versatile Theorem

A Versatile Theorem
URL: http://www.cut-the-knot.org/Curriculum/Geometry/MMParallel.shtml - 23kb - 19 Jun 2006

86. Isogonal and Isotomic Conjugalities

Isogonal and Isotomic Conjugalities: if the cevians of three points on the sides of a triangle concur, so do their conjugates. If the points are collinear, so are their conjugates.
URL: http://www.cut-the-knot.org/Curriculum/Geometry/Conjugality.shtml - 23kb - 19 Jun 2006

87. Centroids in Polygon

Centroids in Polygon: in any N-gon, the N-gon formed by the barycenters N-1 successive vertices is homothetic to the original polygon in there common center of gravity
URL: http://www.cut-the-knot.org/Curriculum/Geometry/CentroidsInPolygon.shtml - 23kb - 19 Jun 2006

88. Feuerbach's Theorem: What Is It About?

Feuerbach's Theorem: 9-point circle is tangent to the incircle and the three excircles
URL: http://www.cut-the-knot.org/Curriculum/Geometry/Feuerbach.shtml - 23kb - 19 Jun 2006

89. Cevian Nest

Cevian Nest. If two triangles are perspective to a third, they are perspective to each other.
URL: http://www.cut-the-knot.org/Curriculum/Geometry/CevaNest.shtml - 23kb - 19 Jun 2006

90. Asymmetric Propeller

Asymmetric Propeller: What is it?
URL: http://www.cut-the-knot.org/Curriculum/Geometry/AsymmetricPropeller2.shtml - 23kb - 19 Jun 2006

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