Circles: Table of Content (Page 1 of 5)

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GoGeometry New website and domain for Geometry from the Land of the Incas.

115.

Stonehenge builders had geometry skills to rival Pythagoras
Five years of detailed research, carried out by the Oxford University landscape archaeologist Anthony Johnson, claims that Stonehenge was designed and built using advanced geometry.

114.

Eight-Point Circle Theorem
Step-by-Step construction, Manipulation, and animation.

113.

Proposed Problem 100. Circle Area, Archimedes' Book of Lemmas.

112.

Proposed Problem 99: Circle Area, General Extension to Pythagoras' Theorem.

111.

Proposed Problem 96. Similar Triangles, Incenters, Parallelogram.

110.

Proposed Problem 95. Similar Triangles, Inradii, Parallel.

109.

Proposed Problem 94. Similar Triangles, Circumcircles, Circumradii.

108.

Proposed Problem 93. Similar Triangles, Circumcircles, Parallelogram.

107.

Proposed Problem 92. Similar Triangles, Circumcircles, Circumradii, Parallel.

106.

Proposed Problem 86. Intouch and Extouch Triangles, Areas

105.

Proposed Problem 85. Contact Triangles Areas, Incircle, Excircle.

104.

Proposed Problem 84. Contact Triangles Areas, Incircle, Excircle, Inradius, Exradius.

103.

Proposed Problem 83. Area of the Excircle Contact Triangle, exradius, circumradius.

102.

Proposed Problem 82: Triangle. Area of the Contact Triangle, inradius, circumradius.

102.

Proposed Problem 81: Triangle. Area of a triangle, side, inradius, circumradius.

101.

Proposed Problem 80: Triangle. Area of a triangle, side, incircle, inradius.

100.

Feuerbach Points and Nine-Point Circle with interactive animation, manipulation, and step-by-step construction.

99.

Taylor Circle Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.
Henry Martyn Taylor and the blind student of mathematics

98.

Casey's Theorem. Generalized Ptolemy's Theorem.

97.

Proposed Problem 79: Triangle. Similarity, Altitudes, Orthocenter, Incircles, Inradii.

96.

I have used Geometry Expressions, the world's first Interactive Symbolic Geometry System, to visualize the Archimedean Twins and check out a variety of conjectures.

95.

Proposed Problem 78: Angles of a Circle. Perpendicular and parallel lines, Midpoint, Diameter, Chord, Cyclic quadrilateral, Congruence.

94.

Proposed Problem 77: Angles of a Circle. Parallel lines, Cyclic quadrilateral.

93.

Proposed Problem 76: Area of a Circle. Square, Circle, Circular Sector.

92.

Proposed Problem 75: Three Intersecting Circles. Cyclic quadrilateral, Angles.
Acquire and demonstrate mathematical reasoning ability when solving problems.

91.

Proposed Problem 74: Three Intersecting Circles. Cyclic quadrilateral, Angles.
 

90.

Proposed Problem 73: Three Intersecting Circles. Cyclic quadrilateral.
 

89.

Proposed Problem 72: Intersecting Circles. Cyclic quadrilateral, Chords, Parallel.
 

88.

Proposed Problem 71: Cyclic Quadrilateral.

87.

Schiffler Point: Four Euler Lines with interactive animation and manipulation.

86.

Proposed Problem 68: Triangle, Incircle, Inradius, Tangent, Similarity.
 

85.

Proposed Problem 67: Triangle, Circumcircle, Angles, Cyclic Quadrilateral.

84.

Proposed Problem 66: Triangle, Excircle, Tangents, Geometric Mean.
 

83.

Proposed Problem 63: Heptagon Regular, Side and Diagonals.

82.

Proposed Problem 62: Square Diagonal, Inscribed Circle.

81.

Incenter, Excenter, Incircle, Excircle Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulation, and animation.

80.

Four Circles Theorem Using TracenPoche Dynamic Software
Step-by-Step construction, Manipulate, and animation.

79.

Three Tangent Circles Theorem Using TracenPoche Dynamic Software 
Step-by-Step construction, Manipulate, and animation.

78.

Three Circles Theorem Using TracenPoche Dynamic Software

77.

Arbelos, Inscribed Circle and Concyclic Points Cyclic Quadrilateral

76.

Feuerbach Theorem
One of the most striking theorems in triangle geometry.

75.

Feuerbach Point Facts
 

74.

Feuerbach Theorem, Acute Triangle illustration
 

73.

Feuerbach Theorem, Obtuse Triangle illustration
 

72.

Hippocrates and Squaring the Circle
 

71.

Lunes of Hippocrates 4
 

70.

Lunes of Hippocrates 3
 

69.

Lunes of Hippocrates 2
 

68.

Lunes of Hippocrates 1
 

67.

Pythagoras and Circle Area
 

66.

Brahmagupta's Theorem Cyclic quadrilateral.

65.

Brahmagupta's Corollary Cyclic quadrilateral.

64.

Brahmagupta's Formula  Area of a cyclic quadrilateral.

63.

Mascheroni Construction with compass alone. Midpoint of a segment

62.

Sangaku Proposed Problem 41. "Mickey Mouse."
Three circles, tangents, radii.